Question

Let $f(x)=\sin x .$ What is the value of $f^{\prime}(\pi) ?$

   Let $f(x)=\sin x .$ What is the value of $f^{\prime}(\pi) ?$

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle… 1st Edition

Chapter 3, Problem 5

Instant Answer

Solved by Expert Ernest Castorena

05/27/2020

Step 1

The derivative of $\sin x$ is $\cos x$. So, $f'(x) = \cos x$. Show more…

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Let $f(x)=\sin x .$ What is the value of $f^{\prime}(\pi) ?$

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Key Concepts

Derivative

A derivative represents the instantaneous rate of change of a function with respect to its variable. It is a central concept in calculus and is defined as the limit of the ratio of the change in the function value to the change in the input variable as this change approaches zero.

Differentiation of Trigonometric Functions

Trigonometric functions have specific differentiation rules that are essential in calculus. For example, the derivative of the sine function is the cosine function. These rules are instrumental in solving problems involving periodic phenomena and oscillations.

Evaluation of the Derivative at a Specific Point

After determining the derivative of a function, evaluating it at a particular point involves substituting the point's value into the derivative. This process helps in finding the specific rate of change of the function at that single point, which is useful for understanding local behavior or solving applied problems.

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