Question

If f(x)=e^2x and g(x)=lnx, then the derivative of y=f(g(x)) at x=e is
Answer: 2e
How do you get to this answer? Please explain.

Answer 1

whats f(g(x)) you got ?

Answer 2

f(g(x)) is when you put g(x) as x in f(x)

Answer 3

so i put g(x) into f(x) and got y=2x

Answer 4

thats correct! :)
what its derivative

Answer 5

then do i just put e in for x?

Answer 6

i think you got
y=x^2
then its derivative
dy/dx = 2x
right ?

Answer 7

and yes, then you just put x= e :)

Answer 8

oh that's so much easier than i thought. thanks again :)

Answer 9

welcome ^_^