# Homework Help: Finding composite derivatives

1. Apr 26, 2010

### steve snash

1. The problem statement, all variables and given/known data
a) (f ° g)′(−2) = ?
b) (g ° f)′(2) = ?

2. Relevant equations
f(−2) = −3,
g(−2) = −4,
f(2) = 3,
g(2) = −3,
f ′(−2) = −1,
f ′(−4) = −2,
f ′(2) = 5,
g ′(−2) = 1,
g ′(2) = 2,
g ′(3) = −4.

3. The attempt at a solution
I have no idea how to do it every thing ive tried doesnt work, how do you work it out. Could someone explain the processes so i know how to do any derivative of a composite function

2. Apr 26, 2010

### gabbagabbahey

Just use the chain rule...

$$(f\circ g)(x)=f(g(x))\implies\frac{d}{dx}(f\circ g)(x)=\frac{d}{dx}f(g(x))=\frac{df(g)}{dg}\frac{dg}{dx}=f'(g(x))g'(x)=(f'\circ g)(x)g'(x)$$

3. Apr 26, 2010

### lanedance

i would take the composition of functions to mean:
$$f \circ g(x) = f(g(x))$$

using the chain rule, what is
$$\frac{d}{dx}f(g(x))=?$$

4. Apr 26, 2010

### steve snash

that makes the answer (f o g)'(-2)= f(-2)(g(-2))(g'(-2))
= -1(-4)x(1)
which = 4 which is the wrong answer =(

5. Apr 26, 2010

### gabbagabbahey

No, $(f'\circ g)(-2)=f'(g(-2))=f'(-4)$