Question

Question #3df2a

Answer 1

Answer: `d/(dx)sqrt(x^2+4)=x/sqrt(x^2+4)`

Explanation:

Assuming the question meant "differentiate" using the chain rule rather than "derive" the chain rule.

Differentiate `sqrt(x^2+4)`

Note that the chain rule states that for a composition of functions:
`h(x)=f(g(x))`
The derivative of `h(x)` would be:
`h'(x)=f'(g(x))*g'(x)`

First, we note that:
`sqrt(x^2+4)=(x^2+4)^(1/2)`

In this problem, we apply the chain rule.
We notice that in this case, `f(x)=sqrt(x)` and `g(x)=x^2+4`, so:
`d/(dx)(x^2+4)^(1/2)=1/2(x^2+4)^(-1/2)(2x)`
`d/(dx)(x^2+4)^(1/2)=x/sqrt(x^2+4)`