function problemss 31

**doboy** · Oct 21st 2010, 09:15 AM

If F(x) = f( 2f( 4f( x ))), where f(0) = 0 and f '(0) = 3, find F '(0).

**Also sprach Zarathustra** · Oct 21st 2010, 09:28 AM

Try to find F'(x)...

Show your work.

**doboy** · Oct 21st 2010, 07:52 PM

i am learning derivatives rite now and i have to use the information available and solve it.. i don't have an idea.. confused.. can some one else please help me with it !!

**TheEmptySet** · Oct 21st 2010, 09:07 PM

Originally Posted by doboy

If F(x) = f( 2f( 4f( x ))), where f(0) = 0 and f '(0) = 3, find F '(0).

let $w=4f(x)$
$u=2f(w)$ then

$F(x)=f(u)$

Now by the chain rule you get

$\frac{dF}{dx}=\frac{df}{du}\frac{du}{dw}\frac{dw}{ dx}=...$

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