Show that the derivative of y = tan x is y′=ddxtanx=sec2x
Solution y′=ddxtanx=↑Identityddxsinxcosx=↑Quotient Rule[ddxsinx]cosx−sinx[ddxcosx]cos2x=cosx⋅cosx−sinx⋅(−sinx)cos2x=cos2x+sin2xcos2x=1cos2x=sec2x