Derivation by first principles: cos(x^0.5)

[PedroB]

Homework Statement

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

Homework Equations

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

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

 

[pasmith]

Homework Statement

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

Homework Equations

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

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

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