Question

Let f(x) be a polyomial in x. Then the second order derivative of f(e^x), is –

• A. f´′(e^x).e^x + f′(e^x)
• B. f´′(e^x).e^2x + f ′(e^x) . e^2x
• C. f´′(e^x)e^2x
• D. f´′(e^x)e^2x + f ′(e^x).e^x

Answer 1

Answer: (D)

f´′(e^x)e^2x + f ′(e^x).e^x

Answer 2

If y = f(e^x)

$\frac{dy}{dx}$ = f´(e^x) × e^x (By U.V)

Second Derivative $\frac{d^{2}y}{dx^{2}}$ = f´´(e^x) . e^2x + e^x f´(e^x)