Higher Order Derivatives

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If y = x⁴, then d²y/dx² equals

RankGuru · Accepted Answer

1. **First Derivative ($y'$)**: Apply power rule once.
   - $\frac{dy}{dx} = 4x^3$.
2. **Second Derivative ($y''$)**: Differentiate the first derivative again.
   - $\frac{d^2y}{dx^2} = \frac{d}{dx}(4x^3)$
   - Apply power rule again: $4 \cdot (3x^{3-1}) = 12x^2$.
3. **Result**: $y'' = 12x^2$.

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Higher Order Derivatives

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