Question

If F(x) = f(3f(5f(x))), where f(0) = 0 and f '(0) = 2, find F '(0).

Answer 1

I had to squint my eyes at this one for a second with all the nested parenthesis.

Basically you need to use the chain rule a bunch of times to obtain an expression for F'(x). Once you have that, wherever you see f'(0), substitute '2' and there's your answer. :)

Answer 2

thank you! but can you show me step by step with the answer?

Answer 3

Let's break it down a bit... can you take the derivative of y = f(5f(x)) using the chain rule?

Answer 4

My teacher didn't clearly teach the chain rule so I really do not know.

Answer 5

Youtube user PATRICKJMT is awesome: http://youtu.be/6kScLENCXLg
Paul's Online Math Notes are BOSS: http://tutorial.math.lamar.edu/Classes/CalcI/ChainRule.aspx

Khanacademy has tons of practice problems http://www.khanacademy.org

and the Temple COW has lots of problems for free with no sign up:

1.Calculus Book I > 4.Techniques and Theory of Differentiation > 3.Chain Rule

http://cow.temple.edu/

:)

Answer 6

It is bedtime for me, have a good night and good luck!