Compute d/dx(f(g(x)))

Question

-where f(x)= square root of x
-and g(x)=x^2+7

Answer 1

f(g) = √g = √(x^2+7)

so, d/dx f(g(x)) = x/√(x^2+7)

Or, using the chain rule,

d/dx f(g) = df/dg * dg/dx
= 1/2√g * 2x
= x/√g
= x/√(x^2+7)