# Homework Help: Derivation by first principles: cos(x^0.5)

1. Aug 28, 2013

### PedroB

1. The problem statement, all variables and given/known data

Find the derivative of the function f(x)=cos(√x) by first principles

2. Relevant equations

f'(x)= lim as h tends to zero of [f(x+h)-f(x)]/h

3. The attempt at a solution

Problems arise immediately, since I have no idea what to do with the expression cos(√(x+h)), I've tried binomial expansion, but to no avail. Any help would be greatly appreciated

2. Aug 28, 2013

### pasmith

$$\cos(\sqrt{x + h}) = \cos(\sqrt{x}(1 + h/x)^{1/2})$$
and keep the first two terms of the binomial expansion of $(1 + h/x)^{1/2}$.