Thread: function problemss 31

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

Try to find F'(x)...

Show your work.

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 !!

Originally Posted by doboy

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

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

$\displaystyle F(x)=f(u)$

Now by the chain rule you get

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