Question

@Michele_Laino

Answer 1

wait a moment please, I'm trying...

Answer 2

I think that the answer is 6, is it right?

Answer 3

sorry not 6, it is 30

Answer 4

wait I have made an error another time, it is 2*4*3=24, it is right I thinkl!

Answer 5

you have to apply the chain rule in order to calculate the derivative of the function of function g(f(2x)

Answer 6

can you show me and explain like the other questions??

Answer 7

ok!

Answer 8

have to calculate this derivative:
d/dx(g(f(2x), now I perform a change of variable, namely z=2x, so our derivative will be:
\[\frac{ d g(f(2x))}{ dx }=2\frac{ dg(f(z) }{ dz }\]
at point z=2x=2*1=2

Answer 9

now, applying the chain rule we have:
\[2\frac{ dg }{ df }\frac{ df }{ dz }\]
when z=2, now,
when z=2, f(2)=1, f'(2)=3 and g'(1)=4, from your table,
so the derivative dg/dz has to be calculate at point f(2)=1, namely g'(1)=4.
Substituting all those numerical data, we get:
your derivative=2*4*3=24

Answer 10

thanks!!!