Question

prove, that if f(x)=cos(x), then f'(x)=-sin(x)

Answer 1

See attached file.
1. Create difference quotient
2. Use trigonometric identity to simplify.
3. Use facts that limit [cosx -1]/x = 0 as x--->0 and limit [sinx/x] =1 as x--->0
to simplify.

Answer 2

use 1st principle.... y'=lim h ->0 [{f(x+h)-f(x)}/h] .... solve the limit..