Question

If y= 2f(g(x)), then d^2y/dx^2=​

Answer 1

Use the chain rule to differentiate both sides of the given equation with respect to $x$ :

$y = 2 f(g(x))$

$\dfrac{dy}{dx} = y' = 2 f'(g(x)) g'(x)$

Differentiate again with the product and chain rules to get the second derivative :

$\dfrac{d^2y}{dx^2} = y'' = \boxed{2 f'(g(x)) g''(x) + 2 f''(g(x)) g'(x)^2}$

(D)