How do you differentiate f(x)=cos(x^2-4x) f(x)=cos(x24x) using the chain rule?

1 Answer
May 6, 2016

d y=-(2x-4)*sin(x^2-4x)*d xdy=(2x4)sin(x24x)dx

Explanation:

f(x)=y=cos(x^2-4x)f(x)=y=cos(x24x)

u=x^2-4xu=x24x

y=cos u

(d u)/(d x)=2x-4dudx=2x4

(d y)/(d u)=-sin u=-sin(x^2-4x)dydu=sinu=sin(x24x)

(d y)/(d x)=(d u)/(d x)*(d y)/(d u)dydx=dudxdydu

(d y)/(d x)=-(2x-4)*sin(x^2-4x)dydx=(2x4)sin(x24x)

d y=-(2x-4)*sin(x^2-4x)*d xdy=(2x4)sin(x24x)dx