### Home > CALC > Chapter 7 > Lesson 7.3.3 > Problem 7-137

7-137.

Given:

*f*(*x*) and*g*(*x*) continuous and differentiable such that*f*(*g*(*x*)) =*x.*Homework Help ✎Evaluate.

*f*′(*g*(0))*g*′(1)*g*′(2)*f*′(*g*(2))3 ·

*f*′(2)5 ·

*f*′(1) + 6 ·*g*′(1)

*x**f*(*x*)*f*′(*x*)*g*(*x*)–1

2

1

0

0

–1

2

2

1

1

7

1

2

0

3

–1

Since *g*(2) = −1,

the inverse, *f*(−1) = 2.

Now *f* '(−1) = 1, so *g* '(2) = __

Refer to the hint in part (b)

Refer to the hint in part (b).

How to find derivative of inverse functions:

A function, *f*, and its inverse, *g*, will have reciprocal derivatives at corresponding (*x*, *y*)→(*y*, *x*) values.