AP Calculus AB : Understanding the derivative of trigonometric functions

Example Questions

Example Question #1 : Understanding The Derivative Of Trigonometric Functions

Find the derivative of the following function:

Explanation:

The derivative of  is. It is probably best to memorize this fact (the proof follows from the difference quotient definition of a derivative).

Our function

the factor of 3 does not change when we differentiate, therefore the answer is

Example Question #2 : Understanding Derivatives Of Trigonometric Functions

Explanation:

The derivative of a sine function does not follow the power rule. It is one that should be memorized.

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Example Question #1 : Specific Derivatives

What is the second derivative of ?

Explanation:

The derivatives of trig functions must be memorized. The first derivative is:

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To find the second derivative, we take the derivative of our result.

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Therefore, the second derivative will be .

Example Question #1 : Derivative Review

Find the derivative of the function

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Explanation:

We can use the Chain Rule:

Let , so that .

Example Question #3 : Understanding Derivatives Of Trigonometric Functions

Compute the derivative of the function .