How do you differentiate y =cos(3sqrtx+7) using the chain rule?

1 Answer
Dec 31, 2015

Remembering that chain rule states that (dy)/(dx)=(dy)/(du)(du)/(dx), we can rename u=3sqrt(x)+7.

Explanation:

Now, let's do it, considering y=cos(u) and u=3sqrt(x)+7:

(dy)/(dx)=sin(u)*3/(2sqrt(x))=sin(3sqrt(x)+7)*3/(2sqrt(x))

(dy)/(dx)=(3sin(3sqrt(x)+7))/(2sqrt(x))