Question

Suppose g is a differentiable function, where g(1)=-2 and g'(1)=5. Find d/dx(g(x^2)/(x^2)) when x=1.

Answer 1

\[g \prime (g(x^2)/x^2) \] when x=1

Answer 2

well, we have a chain rule to apply and a product rule

[g(x^2) * x^-2]' = g(x^2)' * x^-2 + g(x^2) * x'^-2