CPM Homework Help : CALC Problem 4-31

CPM Homework Banner

Home > CALC > Chapter 4 > Lesson 4.1.3 > Problem 4-31

4-31.

Differentiate the following with respect to $x$ . That is, find $\frac { d y } { d x }$ .

$y = \frac { x + 1 } { x }$
Steps (a):
Simplify the fraction:
$y=1+\frac{1}{x}$
$= 1 + x^{-1}$
Answer (a):
Differentiate:
$\frac{dy}{dx}=-x^{-2}$
$=-\frac{1}{x^{2}}$

$y =\operatorname{cos }x +\operatorname{sin }x$
Hint (b):
Be careful about $+$ and $−$ signs.

$y = x \cdot \sqrt [ 3 ] { x ^ { 2 } }$
Hint (c):
Before you differentiate, rewrite with exponents.

$y = (6-5x)(1-2x)$
Hint (d):
Before you differentiate, expand.

© 2022 CPM Educational Program. All rights reserved.