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))`

`(dy)/(dx) = y' = 2 f'(g(x)) g'(x)`

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

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

(D)