Differentiating trigonometric function

Intro

(1) d/dx(sinx)= cosx
(2) d/dx(cosx)= -sinx
(3) d/dx(tanx)= -( secx)2
(4) d/dx(cotx)= -(cosecx)2
(5) d/dx(secx)= secx.tanx
(6) d/dx(cosecx)= -cosecx.cotx

Sample Problem

Solution

Let y=tan(3π/2+x)
dy/dx=(sec(3π/2+x))2— differentiate
dy/dx( at x=π/4)=(sec(3π/2+π/4)2— substituting x=π/4
=(sec(7π/4))2
= ( sec(2π-π/4))2 —simplify
=(sec(π/4))2
=1/(cos(π/4))2
=1/(1/2)
=2