Question

Use the Chain Rule to find the derivative. $$ y=\sin ^{2} x $$

   Use the Chain Rule to find the derivative.
$$
y=\sin ^{2} x
$$

Calculus for AP

Calculus for AP

Jon Rogawski & Colin… 3rd Edition

Chapter 3, Problem 30

Instant Answer

Solved by Expert Linh Vu

10/17/2020

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Here, the function is $\sin^2x$ and its derivative is $2\sin x \cos x$. Show more…

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Use the Chain Rule to find the derivative. $$ y=\sin ^{2} x $$

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Key Concepts

Chain Rule

The chain rule is a fundamental theorem in calculus for differentiating composite functions. It states that if a function can be expressed as a composition of two functions, f(g(x)), then its derivative is f'(g(x)) multiplied by g'(x). This concept enables the differentiation of complex functions by breaking them into simpler parts.

Differentiation of Trigonometric Functions

When differentiating trigonometric functions, specific rules apply, such as the derivative of sin(u) being cos(u) multiplied by the derivative of u. This concept is crucial for handling functions where a trigonometric expression is composed with another function.

Differentiation of Polynomial Functions

Polynomial functions are commonly differentiated using the power rule, which states that the derivative of x^n is n*x^(n-1). This rule is essential when the inner function of a composite function is a polynomial, allowing for straightforward computation of its derivative.

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