【webwork】 Chapter 3.2 solutions.－Josephood7

Differentiate:

g (x) = x \sqrt 10 e x

$g^{'} (x) =$

Find the derivative of the function

g (x) = e x 2 x + 2

$g^{'} (x) =$

If $f$ is a differentiable function, find an expression for the derivative of each of the following functions:

In submitting the answers below, write $f (x)$ as $f$ , and write $f^{'} (x)$ as $g$ .

(a) If $y = x^{2} f (x)$ , then $y^{'} =$

(b) If $y = \frac{f (x)}{x^{2}}$ , then $y^{'} =$

(d) If $y = \frac{1 + x f (x)}{\sqrt{x}}$ , then $y^{'} =$

Let $P (x) = F (x) G (x)$ and $Q (x) = F (x) / G (x)$ , where $F (x)$ and $G (x)$ are the functions whose graphs are shown.

(a) Find $P^{'} (2)$ :

(b) Find $Q^{'} (7)$ :

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