Question

Let the function f(x) have the property that f′(x)=(x+1)/(x−3). If g(x)=f(x^2) find g′(x)

Answer 1

Solve this using chain rule:
Start with g(x) = f(x^2), Differentiate both sides:
$g'(x) = f'(x^2) * (x^2)' \\ \\ g'(x) = 2x f'(x^2)$

Now sub in "x^2" into given f'(x) function:
$g'(x) = 2x*\frac{ x^2 +1}{x^2 -3}$