DIFFERENTIATION PART 3: HOW TO DIFFERENTIATE TRIGONOMETRIC FUNCTION WITH THE CALCULATOR

Darling Fee
7 Jan 202317:31
EducationalLearning
32 Likes 10 Comments

TLDRThe video script is a tutorial on using a calculator to solve differentiation problems involving trigonometric functions. It emphasizes setting the calculator to radian mode and demonstrates step-by-step instructions for differentiating expressions like e^(sin(x)), cos(Ο€/4 - 2x), and e^x/(1 + e^x). The presenter guides viewers through entering expressions, performing differentiation, and comparing results with potential answers to identify the correct one. The tutorial aims to simplify the learning of mathematics, particularly differentiation, by leveraging calculator functions.

Takeaways
  • πŸ“š The video is a tutorial on using a calculator to solve differentiation problems, specifically those involving trigonometric functions.
  • πŸ”’ To begin, ensure the calculator is set to radian mode by pressing shift, mode, and selecting option four for trigonometric and exponential functions.
  • πŸ“ The process involves using the differential button, which is accessed by pressing shift and the integral sign to initiate differentiation.
  • πŸ”‘ When differentiating expressions, it's important to correctly input the function into the calculator, including brackets and exponents.
  • ⚠️ After inputting the expression, ensure to close any opened brackets to avoid errors.
  • 🎯 Differentiate the expression with respect to 'x' by moving the cursor and inputting '1' where specified, then press the equal sign to get the result.
  • πŸ’Ύ To compare answers, save the result of the differentiation in memory register 'E' by using shift, store, and then 'E'.
  • πŸ” To check possible answers, input them into the calculator without differentiating, then use the calc button to evaluate at the same value used in the original differentiation.
  • πŸ“‰ If the calculated value divided by the saved value in 'E' equals one, the entered expression is the correct derivative.
  • πŸ“ˆ The tutorial demonstrates solving multiple questions, including those with exponential and trigonometric components, and comparing answers to find the correct derivative.
  • πŸ“š The script emphasizes practice and careful entry of expressions into the calculator as key to successfully using the tool for differentiation.
Q & A

  • What is the first step to solve trigonometric differentiation using a calculator according to the script?

    -The first step is to set the calculator to the radiant mode by pressing shift, then mode, and selecting option four.

  • How do you differentiate an expression involving trigonometric functions on the calculator?

    -You press shift, then the integral sign to bring up the differential symbol, and then enter the expression to be differentiated.

  • What does the script suggest to do after setting up the calculator in radiant mode?

    -The script suggests differentiating the expression with respect to 'x' by pressing the differential button and entering the expression.

  • How do you indicate an exponent on the calculator as demonstrated in the script?

    -You indicate an exponent by pressing shift and then 'e' for the exponential symbol, followed by the base and the '^' symbol for exponentiation.

  • What is the process to differentiate an expression with respect to 'x' equal to one as per the script?

    -Move the cursor to the right-hand side, replace the box with '1', and press the equal sign button to get the differentiated result.

  • Why do we save the differentiated answer in 'E' according to the script?

    -We save the differentiated answer in 'E' to compare it with possible answers to determine which one matches the correct differentiation result.

  • What does the script suggest to do to check if a possible answer is correct after differentiation?

    -Enter the expression of the possible answer into the calculator, use the calc button, and then divide the result by the saved answer in 'E' to see if it equals one.

  • How does the script guide you to determine the correct differentiation of 'e^(sin(x))'?

    -By differentiating the expression with respect to 'x' equal to one, saving the result in 'E', and then checking if the division of the calculated result by the saved result equals one.

  • What is the method to solve for 'F Prime' as described in the script?

    -Ensure the calculator is in radiant mode, use the differential symbol, enter the function, and differentiate at a value of 'x' equal to one.

  • How do you ensure that the entered expression on the calculator matches the one in the question according to the script?

    -After entering the expression, cross-check it to make sure it is correct before pressing the calc button and using the value used in differentiation.

  • What is the final step to confirm the correct answer for a differentiation problem as per the script?

    -Divide the calculated result by the saved answer in 'E' (or 'A'/'P' for other examples), and if the result is one, it confirms the answer is correct.

Outlines
00:00
πŸ“š Introduction to Using a Calculator for Trigonometric Differentiation

The speaker, Darling V, introduces a tutorial on how to use a calculator to solve differentiation problems involving trigonometric functions. The focus is on setting the calculator to radian mode by pressing shift, mode, and selecting option four. The demonstration includes differentiating an expression with an exponential function of sine, writing the expression on the calculator, and solving for differentiation at x equals one. The result is saved in the calculator's memory for comparison with possible answers.

05:02
πŸ” Verifying the Correct Differentiation Answer Using Calculator

The video script continues with a step-by-step guide on how to verify the correct answer for a differentiation problem using a calculator. It explains the process of entering the differentiated expression into the calculator and using the calc button to solve for x equals one. The result is then compared with a saved value in the calculator's memory to determine correctness. The method is applied to differentiate 'Y = e^(sin x)' and to verify the correct answer, which turns out to be 'e^(sin x) * cos x'.

10:04
πŸ“˜ Differentiating a Trigonometric Function with a Calculator

The script describes the process of differentiating a function 'f(x) = cos(Ο€/4 - 2x)' using a calculator set in radian mode. It details entering the function into the calculator, differentiating it at x equals one, and saving the result. The correct differentiation answer is then identified by comparing it with possible answers, which involves solving the non-differentiated form of the answer with x equals one and checking if it matches the saved differentiated result.

15:06
πŸ“™ Solving for the Correct Derivative of an Exponential Function

The final paragraph of the script outlines the steps to differentiate 'e^x / (1 + e^x)' at x equals one using a calculator. It includes entering the function correctly, differentiating at the specified value, and saving the result. The script then guides through checking the possible answers by solving them with the same value used for differentiation and comparing with the saved result to find the correct derivative.

Mindmap
Keywords
πŸ’‘Differentiation
Differentiation in the context of the video refers to the mathematical process of finding the derivative of a function with respect to a variable. It is a fundamental concept in calculus and is essential for understanding rates of change and slopes of curves. The video's theme revolves around teaching viewers how to use a calculator to perform differentiation, particularly for trigonometric functions.
πŸ’‘Calculator
A calculator is an electronic device used for performing arithmetic operations and more complex calculations. In the video, the calculator is used as a tool to simplify the process of differentiation. The script provides step-by-step instructions on how to set the calculator to radian mode and use its differentiation functions, highlighting its importance in making mathematical learning easier.
πŸ’‘Radian Mode
Radian mode is a setting on scientific calculators that allows for calculations to be performed using radians instead of degrees. This is crucial when dealing with trigonometric functions, as radians are the standard unit for these calculations. The video instructs viewers to set their calculators to radian mode before solving trigonometric differentiation problems.
πŸ’‘Trigonometric Functions
Trigonometric functions are mathematical functions that relate the angles of a triangle to the lengths of its sides. They include sine, cosine, and tangent, among others. In the video, the presenter teaches how to differentiate expressions involving trigonometric functions using a calculator, emphasizing the relevance of these functions in calculus.
πŸ’‘Exponential Function
An exponential function is a mathematical function of the form f(x) = a^x, where 'a' is a constant. The video mentions exponential functions in the context of differentiation, showing how to differentiate expressions like e^(sin(x)) using a calculator, which demonstrates the versatility of the calculator in handling different types of functions.
πŸ’‘Natural Log
Natural log, or the logarithm to the base e, is a mathematical function that is the inverse of the exponential function. It is denoted as ln(x). In the video script, the natural log is used as part of the process to enter exponential expressions into the calculator for differentiation purposes.
πŸ’‘Differential Button
The differential button on a scientific calculator is used to initiate the process of differentiation. The video script describes how to use this button by pressing 'shift' and then the integral sign to bring up the differentiation symbol on the calculator, which is the first step in differentiating an expression.
πŸ’‘Exponent
An exponent is a number that indicates how many times a base number is multiplied by itself. In the context of the video, exponents are used in expressions like e^(sin(x)) and are differentiated using the calculator. The script provides examples of how to input exponents into the calculator for differentiation.
πŸ’‘Brackets
Brackets are used in mathematical expressions to group terms together, indicating that operations within the brackets should be performed before those outside. The video script mentions the importance of opening and closing brackets correctly when entering expressions into the calculator to avoid errors.
πŸ’‘Store Function
The store function on a calculator allows users to save the result of a calculation for later use. In the video, the presenter demonstrates how to use the store function to save the result of a differentiation step, which can then be compared with potential answers to verify the correct solution.
πŸ’‘Calc Button
The calc button on a calculator is used to perform calculations based on the expression entered. In the video, the calc button is used after entering a potential answer to determine if it matches the saved result from the differentiation process, helping to identify the correct answer.
Highlights

Introduction to using a calculator for differentiation involving trigonometric functions.

Setting the calculator to radian mode for trigonometry problems by pressing shift, mode, and selecting option four.

Differentiation of an expression with e^(sin(x)) using the calculator's differential button.

Writing the expression e^(sin(x)) on the calculator and differentiating it with respect to x=1.

Saving the differentiation result in the calculator's memory for later comparison.

Comparing possible answers by entering them as expressions on the calculator and using the calc button.

Determining the correct differentiation answer by dividing the new answer by the saved one in memory.

Differentiating the function f(x) = cos(Ο€/4 - 2x) to find F' using the calculator.

Entering fractions and exponents correctly on the calculator for accurate differentiation.

Differentiating at a specific value (x=1) and saving the result for comparison with possible answers.

Cross-checking entered expressions on the calculator before solving to ensure accuracy.

Using the calc button to solve expressions and compare with saved differentiation results.

Differentiating e^x / (1 + e^x) and identifying the correct answer by comparing with the saved result.

Practicing calculator differentiation to master the process for various functions.

The importance of closing brackets when entering expressions on the calculator to avoid errors.

Utilizing the calculator's memory to store and retrieve differentiation results for verification.

Demonstration of step-by-step differentiation using a calculator for better understanding.

Transcripts

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DifferentiationTrigonometryCalculatorMath TutorialEducationalExponential FunctionsNatural LogRadiant ModeSolving EquationsLearning Tools