Find \(\rm \frac{d^2 (x^{10})}{dx^2}\)

  1. 10(x9)
  2. 90(x8)
  3. 90(x9)
  4. None of these

Answer (Detailed Solution Below)

Option 2 : 90(x8)
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Detailed Solution

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Concept:

\(\rm \frac{dx^{n}}{dx}= nx^{n-1}\)

Calculation:

To Find: \(\rm \frac{d^2 (x^{10})}{dx^2}\)

\(\rm \frac{d^2 (x^{10})}{dx^2} = \frac{d}{dx} \left(\frac{dx^{10}}{dx} \right )\)

\(\rm = \frac{d}{dx} (10x^{9})= 10 \frac{dx^{9}}{dx}\)

= 10 × 9 × x8

= 90(x8)

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