Question

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

Answer 1

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))`