### Home > APCALC > Chapter 4 > Lesson 4.1.3 > Problem4-31

4-31.

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

1. $y = \frac { x + 1 } { x }$

Simplify the fraction:

$y=1+\frac{1}{x}$

$= 1 + x ^{−1}$

Differentiate:

$\frac{dy}{dx}=-x^{-2}$

$=-\frac{1}{x^{2}}$

2. $y=\cos\left(x\right)+\sin\left(x\right)$

Be careful about $+$ and $−$ signs.

3. $y = x \cdot \sqrt [ 3 ] { x ^ { 2 } }$

Before you differentiate, rewrite with exponents.

4. $y = \left(6 – 5x\right)\left(1 – 2x\right)$

Before you differentiate, expand.