Question #3df2a

1 Answer
Jun 1, 2017

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)