How do you differentiate cos(x^2)cos(x2)? Calculus Differentiating Trigonometric Functions Differentiating sin(x) from First Principles 1 Answer Eddie Jul 2, 2016 - 2x sin x^2 −2xsinx2 Explanation: Use the chain rule so y = cos u implies dy/(du) = -sin uy=cosu⇒dydu=−sinu u = x^2 implies (du)/dx = 2xu=x2⇒dudx=2x Chain rule dy/dx = dy/(du)* (du)/dxdydx=dydu⋅dudx = - sin u * 2x = - 2x sin x^2 =−sinu⋅2x=−2xsinx2 Answer link Related questions How do you differentiate f(x)=sin(x)f(x)=sin(x) from first principles? What is the derivative of y=3sin(x) - sin(3x)y=3sin(x)−sin(3x)? How do you find dy/dx if x + tan(xy) = 0x+tan(xy)=0? How do you find the derivative of the function y=cos((1-e^(2x))/(1+e^(2x)))y=cos(1−e2x1+e2x)? How do you differentiate f(x)=2secx+(2e^x)(tanx)f(x)=2secx+(2ex)(tanx)? How do you find the derivate for y = pisinx - 4cosxy=πsinx−4cosx? How do you find the derivative of f(t) = t^2sin tf(t)=t2sint? What is the derivative of sin^2(lnx)sin2(lnx)? How do you compute the 200th derivative of f(x)=sin(2x)f(x)=sin(2x)? How do you find the derivative of sin(x^2+1)sin(x2+1)? See all questions in Differentiating sin(x) from First Principles Impact of this question 40761 views around the world You can reuse this answer Creative Commons License