   Chapter 3.5, Problem 52E

Chapter
Section
Textbook Problem

Find the derivative of the function. Simplify where possible.52. g ( x ) = arccos x

To determine

To find: The derivative of the function.

Explanation

Given:

The function is g(x)=arccosx.

Derivative rules:

(1) Chain rule: If y=f(u) and u=g(x)  are both differentiable function, then

dydx=dydududx.

(2) Derivative of the inverse trigonometric function: ddx(cos1(x))=11x2.

Calculation:

Obtain the derivative of the function.

Consider the function g(x)=arccosx

Differentiate the function with respect to x.

g(x)=ddx(cos1(x))

Let u=x.

g(x)=ddx(cos1(u))

Apply the chain rule (1).

g(x)=ddu(cos1(u))dudx=(11u2)dudx

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