# Derivative Chart and Composite Function

• Aug 26th 2013, 06:34 PM
Jason76
Derivative Chart and Composite Function
Attachment 29064

I understand that $f(g(x))$ means $g(x)$ plugged into the function $f$ (at it's $x$ value). However we don't have the function, only a chart. How to get around this?
• Aug 26th 2013, 07:03 PM
chiro
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))?
• Aug 26th 2013, 08:18 PM
Jason76
Re: Derivative Chart and Composite Function
Quote:

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 $50$, but the chart seems to be saying $30$ If you look at the line for $g(x)$ at $30$, then you get $20$
• Aug 26th 2013, 08:29 PM
chiro
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.
• Aug 26th 2013, 10:15 PM
Jason76
Re: Derivative Chart and Composite Function
Quote:

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.