Question

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

Answer 1

`f'(x)=cosx-sinx-3x^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:

`d/dx(u+v+w...)=(du)/dx+(dv)/dx+(dw)/dx+...`

Thus,

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

`f'(x)=color(red)(cosx)+color(blue)(-sinx)+color(green)(-3x^2)`

`f'(x)=cosx-sinx-3x^2`