2 questions
1. y = (x+(x+x^(1/2))^(1/2))^(1/2)
y' = ?
How do I do this?
and another related question
F(x) = f(xf(xf(x)))
where f(1) = 2, f(2)=3, f'(1) = 4, f'(2) = 5, f'(3) = 6
F'(1) = ?
Help please!
Do you know the chain rule? Just apply the chain rule repeatedly. The final answer should be
$\displaystyle \frac{d}{dx}(f(x f(x f(x)))) = (x (x f'(x)+f(x)) f'(x f(x))+f(x f(x))) f'(x f(x f(x)))$.
I won't do it by hand but you can look here for a complete answer (click "show steps"). Don't just copy the answer - make sure you understand the chain rule, it's important - you'll really have trouble later on if you don't master it now.
Your first question is similar.