Correct Answer - Option 2 : 18x - 10
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 = 3x3 - 5x2 + 2
Differentiating w.r. to x on both side, we get
⇒\(\rm \dfrac {dy}{dx}\) = (3 × 3x2) - (5 × 2x) + 0
⇒ 9x2 - 10x
Again Differentiating w.r. to x on both sides, we get
⇒\(\rm \dfrac {d^2y}{{dx}^2}\) = (9 × 2x) - 10
\(⇒\rm \dfrac {d^2y}{{dx}^2} = 18x - 10\)