How do you differentiate f(x)=cos(x^2-4x) f(x)=cos(x2−4x) using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer ali ergin May 6, 2016 d y=-(2x-4)*sin(x^2-4x)*d xdy=−(2x−4)⋅sin(x2−4x)⋅dx Explanation: f(x)=y=cos(x^2-4x)f(x)=y=cos(x2−4x) u=x^2-4xu=x2−4x y=cos u (d u)/(d x)=2x-4dudx=2x−4 (d y)/(d u)=-sin u=-sin(x^2-4x)dydu=−sinu=−sin(x2−4x) (d y)/(d x)=(d u)/(d x)*(d y)/(d u)dydx=dudx⋅dydu (d y)/(d x)=-(2x-4)*sin(x^2-4x)dydx=−(2x−4)⋅sin(x2−4x) d y=-(2x-4)*sin(x^2-4x)*d xdy=−(2x−4)⋅sin(x2−4x)⋅dx Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of y= 6cos(x^2)y=6cos(x2) ? How do you find the derivative of y=6 cos(x^3+3)y=6cos(x3+3) ? How do you find the derivative of y=e^(x^2)y=ex2 ? How do you find the derivative of y=ln(sin(x))y=ln(sin(x)) ? How do you find the derivative of y=ln(e^x+3)y=ln(ex+3) ? How do you find the derivative of y=tan(5x)y=tan(5x) ? How do you find the derivative of y= (4x-x^2)^10y=(4x−x2)10 ? How do you find the derivative of y= (x^2+3x+5)^(1/4)y=(x2+3x+5)14 ? How do you find the derivative of y= ((1+x)/(1-x))^3y=(1+x1−x)3 ? See all questions in Chain Rule Impact of this question 1754 views around the world You can reuse this answer Creative Commons License