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

1. $y = \frac { x + 1 } { x }$ 

   Steps (a):

   Simplify the fraction:

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

   $= 1 + x ^{−1}$

   Answer (a):

   Differentiate:

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

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

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

   Hint (b):

   Be careful about $+$ and $−$ signs.

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

   Hint (c):

   Before you differentiate, rewrite with exponents.

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

   Hint (d):

   Before you differentiate, expand.