How do you differentiate #sin^2(x) * cos^2(x)#? Calculus Differentiating Trigonometric Functions Differentiating sin(x) from First Principles 1 Answer ali ergin May 21, 2016 #(d y)/(d x)=2 sin x cos^3 x-2 cos x*sin^3 x# Explanation: #y=sin^2 x*cos^2 x# #(d y)/(d x)=(sin^2 x)^'*cos^2 x+(cos^2 x)^'*sin^2 x# #(sin^2 x)^'=2sin x cos x# #(cos^2 x)^'=-2sin x cos x# #(d y)/(d x)=2 sin x cos x* cos^2 x-2 sin x cos x*sin^2 x# #(d y)/(d x)=2 sin x cos^3 x-2 cos x*sin^3 x# Answer link Related questions How do you differentiate #f(x)=sin(x)# from first principles? What is the derivative of #y=3sin(x) - sin(3x)#? How do you find dy/dx if #x + tan(xy) = 0#? How do you find the derivative of the function #y=cos((1-e^(2x))/(1+e^(2x)))#? How do you differentiate #f(x)=2secx+(2e^x)(tanx)#? How do you find the derivate for #y = pisinx - 4cosx#? How do you find the derivative of #f(t) = t^2sin t#? What is the derivative of #sin^2(lnx)#? How do you compute the 200th derivative of #f(x)=sin(2x)#? How do you find the derivative of #sin(x^2+1)#? See all questions in Differentiating sin(x) from First Principles Impact of this question 1686 views around the world You can reuse this answer Creative Commons License