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If y = e5x then \(\rm \frac {d^2 y}{dx^2}\) =
1. 25y
2. 15y
3. 10y
4. 5y

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Correct Answer - Option 1 : 25y

Concept:

Second-order Derivative.

\(\rm \frac {d^2 f(x)}{dx^2} = \) \(\rm \frac {d}{dx} [\frac {d}{dx} f(x)]\)

\(\rm \frac {d}{dx}e^{f(x)} = e^{f(x)} f'(x)\)

Calculations:

y = e5x 

Differentiating w.r. to x on both side, we get

\(\rm \dfrac {dy}{dx} = 5e^{5x}\)

Again Differentiating w.r. to x on both sides, we get

\(\rm \dfrac {d^2y}{{dx}^2} = 5 \times 5e^{5x}\)

\(\rm \dfrac {d^2y}{{dx}^2} = 25y\)

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