Given, y=(√1+cos(x^2)). Find dy/dx by using chain rule.

Question

Given,

y = (√1+cos(x²))

Answer 1

Given, y=(√1+cos(x^2)). Find dy/dx by using chain rule.

Solution:

y=(√1+cos(x^2)) , then y = [ 1+ cos(x²)]^1/2 , dy/dx = 1/2[1+cos(x²)]^1/2-1 [0+2cos(x)(-sin(x)] = 1/2[1+cos(x²)]^-1/2. [ -2sin(x)cos(x)]= -2sin(x)cos(x) / 2[ 1+cos(x²)]^1/2 = - sin(x) cos(x) / √[1+cos(x²)]