# Derivative Chart and Composite Function

• Aug 26th 2013, 05:34 PM
Jason76
Derivative Chart and Composite Function
Attachment 29064

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?
• Aug 26th 2013, 06:03 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, 07:18 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 \$\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\$
• Aug 26th 2013, 07:29 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, 09:15 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.