# How do you differentiate f(x)=sinx+cosx?

Jan 24, 2017

$f \left(x\right) = \sin \left(x\right) + \cos \left(x\right) \implies f ' \left(x\right) = \cos \left(x\right) - \sin \left(x\right)$

#### Explanation:

Since the derivative of a sum is the sum of the derivatives

$f ' \left(x\right) = \left(\sin \left(x\right)\right) ' + \left(\cos \left(x\right)\right) '$

Since $\frac{d}{\mathrm{dx}} \sin \left(x\right) = \cos \left(x\right)$ and $\frac{d}{\mathrm{dx}} \cos \left(x\right) = - \sin \left(x\right)$

We have

$f ' \left(x\right) = \cos \left(x\right) + \left(- \sin \left(x\right)\right) = \cos \left(x\right) - \sin \left(x\right)$