Definition & Proving Differentiability: A Function f at a Point a

[Unusualskill]

(a) State precisely the definition of: a function f is differentiable at a ∈ R.

(b) Prove that, if f is differentiable at a, then f is continuous at a. You may
assume that
f '(a) = lim {f(x) - f(a)}/(x - a)
x→a

(c) Assume that a function f is differentiable at each x∈ R and also f(x) > 0
for all x ∈R. Use the definition of the derivative and standard limit laws to
calculate the derivative of:
g(x) = (f(x))^0.25
in terms of f(x) and f '(x).

I did part a n b . But stuck at part c , can any1 guide me on part (c)?thank you

 

[mathman]

To save writing, let u = f(x). Therefore you want d/dx(u^0.25)={d/du(u^0.25)}{du/dx}=0.25u^(-0.75)u'.

 

[HallsofIvy]

This same question was posted in the "Calculus and Beyond Homework" section and answered there. Unusualsikill, do not post the same thing in more than one section. If a homework section is appropriate, post there only.