# Thread: Derivative Chart and Composite Function

1. ## Derivative Chart and Composite Function

I understand that $\displaystyle f(g(x))$ means $\displaystyle g(x)$ plugged into the function $\displaystyle f$ (at it's $\displaystyle x$ value). However we don't have the function, only a chart. How to get around this?

2. ## Re: Derivative Chart and Composite Function

Hey Jason76.

Hint: Use the chain rule where h'(x) = g'(x)f'(g(x)) (What x corresponds to the one in line with h'(30))?

3. ## Re: Derivative Chart and Composite Function

Originally Posted by chiro
Hey Jason76.

Hint: Use the chain rule where h'(x) = g'(x)f'(g(x)) (What x corresponds to the one in line with h'(30))?
The answer is $\displaystyle 50$, but the chart seems to be saying $\displaystyle 30$ If you look at the line for $\displaystyle g(x)$ at $\displaystyle 30$, then you get $\displaystyle 20$

4. ## Re: Derivative Chart and Composite Function

g(30) = 20, f(20) = 8 with derivatives:
g'(30) = 10, f'(20) = 5 so this means

h'(30) = g'(30)*f'(20) = 10*5 = 50.

5. ## Re: Derivative Chart and Composite Function

Originally Posted by chiro
g(30) = 20, f(20) = 8 with derivatives:
g'(30) = 10, f'(20) = 5 so this means

h'(30) = g'(30)*f'(20) = 10*5 = 50.
ok thanks. Makes sense.