### Home > CALC > Chapter 3 > Lesson 3.3.2 > Problem3-102

3-102.

Find $f ^\prime(x)$ for each of the following functions.

1. $f ( x ) = \frac { 2 } { 3 } ( x - 5 ) ^ { 3 } + x ^ { 2 }$

$f '\left(x\right) = 2\left(x − 5\right)^{2} + 2x$

1. $f ( x ) = \sqrt [ 3 ] { x }$

Before you find the derivative, rename $f(x)$ using laws of exponent.

1. $f ( x ) = \operatorname { sin } \frac { \pi } { 4 }$

Careful. What is $\operatorname{sin}\frac{\pi }{4}$?
Describe the graph of $y=\text{ sin}\frac{\pi }{4}$.
Describe the behavior of its slope.

1. $f ( x ) = \frac { 1 } { ( x + 1 ) ^ { 2 } }$

Refer the the hint in part (b).