Differentiating Trigonometric Functions

Question 1 • AP Calculus AB - MA5186 A

What is the derivative of f(x) = x sin x?

Answer

f ′(x) = x cos x

f ′(x) = sin x + cos x

f ′(x) = sin x + x cos x

f ′(x) = cos x + x cos x

Use the product rule: the derivative of x sin x is (1)(sin x) + x(cos x). Therefore, f′(x) = sin x + x cos x, which is choice C.

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Example Problem: Using Trigonometric Functions and the Quotient Rule

Example Problem: Using Derivatives of Trigonometric Functions in the Real World

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