How do you differentiate #cos(x^2)#? Calculus Differentiating Trigonometric Functions Differentiating sin(x) from First Principles 1 Answer Eddie Jul 2, 2016 #- 2x sin x^2 # Explanation: Use the chain rule so #y = cos u implies dy/(du) = -sin u# #u = x^2 implies (du)/dx = 2x# Chain rule #dy/dx = dy/(du)* (du)/dx# #= - sin u * 2x = - 2x sin x^2 # 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 40138 views around the world You can reuse this answer Creative Commons License