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

1 Answer
Dec 19, 2015

#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#