Question

If g is a twice differentiable function and f(x) = x^2 g(x^2 + 1) , find f ′′ in terms of x, g, g ′ , and g ′′ .

Answer 1

Step 1 :

The function is .

Apply derivative on each side with respect to x.

Apply product rule of derivatives : .

Apply derivative on each side with respect to x.

Solution :