# 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

Homework Helper

## 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 $(1 + h/x)^{1/2}$.

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