How do you differentiate #y = cos^2 (x^2)#? Calculus Differentiating Trigonometric Functions Derivative Rules for y=cos(x) and y=tan(x) 1 Answer Anees Apr 16, 2015 #y'=-4xcos(x^2)(sinx^2)# Solution #y=cos^2(x^2))# Differentiating both sides with respect to # 'x'# #y'=d/dxcos^2(x^2))# #y'=2cos(x^2)d/dx(cosx^2)# #y'=2cos(x^2)(-sinx^2)d/dx(x^2)# #y'=2cos(x^2)(-sinx^2)(2x)# #y'=-4xcos(x^2)(sinx^2)# Answer link Related questions What is the derivative of #y=cos(x)# ? What is the derivative of #y=tan(x)# ? How do you find the 108th derivative of #y=cos(x)# ? How do you find the derivative of #y=cos(x)# from first principle? How do you find the derivative of #y=cos(x^2)# ? How do you find the derivative of #y=e^x cos(x)# ? How do you find the derivative of #y=x^cos(x)#? How do you find the second derivative of #y=cos(x^2)# ? How do you find the 50th derivative of #y=cos(x)# ? How do you find the derivative of #y=cos(x^2)# ? See all questions in Derivative Rules for y=cos(x) and y=tan(x) Impact of this question 20921 views around the world You can reuse this answer Creative Commons License