Let f(4) = 3 and f'(4) = 2. If g(x) = ( x f(x^2) ) / (x^2 + 1), then g'(2) = ?

Question

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Let f(4) = 3 and f'(4) = 2. If g(x) = ( x f(x²) ) / (x² + 1), then g'(2) = ?

Answer 1

You need to differentiate g(x) with respect to x. You should obtain

g'(x) = f(x²)/(x² + 1) + 2x²f'(x²)/(x² + 1) - 2x²f(x²)/(x² + 1)²

From there, you can substitute x = 2 and solve for g'(2) using the given conditions on f(x).