# How do you differentiate f(x)=sinx+cosx-x^3 using the sum rule?

Dec 19, 2015

$f ' \left(x\right) = \cos x - \sin x - 3 {x}^{2}$

#### Explanation:

The sum rule basically states that to find the derivative of a sum, you can take the derivative of each individual part and add them together to find the derivative of the entire function.

In other words:

$\frac{d}{\mathrm{dx}} \left(u + v + w \ldots\right) = \frac{\mathrm{du}}{\mathrm{dx}} + \frac{\mathrm{dv}}{\mathrm{dx}} + \frac{\mathrm{dw}}{\mathrm{dx}} + \ldots$

Thus,

f'(x)=color(red)(d/dx[sinx])+color(blue)(d/dx[cosx])+color(green)(d/dx[-x^3]

$f ' \left(x\right) = \textcolor{red}{\cos x} + \textcolor{b l u e}{- \sin x} + \textcolor{g r e e n}{- 3 {x}^{2}}$

$f ' \left(x\right) = \cos x - \sin x - 3 {x}^{2}$