Question

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

Answer 1

`f(x)=sin(x)+cos(x) => f'(x)=cos(x)-sin(x)`

Explanation:

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

`f'(x)=(sin(x))'+(cos(x))'`

Since `d/dxsin(x)=cos(x)` and `d/dxcos(x)=-sin(x)`

We have

`f'(x)=cos(x)+(-sin(x))=cos(x)-sin(x)`