Question

using first principle find the derivative of square root of cosx

Answer 1

we know from 1st principles
if y=x^n
then dy/dx=nx^(n-1)
now use this
y =root (cosx)=(cosx)^-1/2
dy/dx=-1/2 (cosx)^(-1/2-1).d(cosx)/dx
=-1/2 (cos)^-3/2.(-sinx)
=1/2(cosx)^-3/2.sinx