Find f^'(x) f(x)=2 sin^2 x

Name: Problem 4, Chapter 2: Calculus Early Transcendentals
Uploaded: 2020-08-19T19:44:40-08:00
Duration: 1 min 37 s
Channel: Prakash Hampole
Description: Find f^'(x) f(x)=2 sin^2 x

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Key Concepts

Chain Rule

The chain rule is a method for differentiating composite functions. When a function is composed of an outer function and an inner function, such as a power function applied to a trigonometric function, the derivative is found by differentiating the outer function with respect to the inner function and then multiplying by the derivative of the inner function.

Power Rule

The power rule is used to differentiate functions of the form u^n, where u is a function of x and n is a constant exponent. In the case of a squared function, the derivative is 2u, multiplied by the derivative of u, which is essential when the function involves sin^2 x.

Derivative of Trigonometric Functions

Knowing the derivative of basic trigonometric functions is crucial. For example, the derivative of sin x with respect to x is cos x. This fundamental derivative is used in the differentiation process of functions involving trigonometric operations, particularly when they are composed with other functions.

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