Question:
If \( y = x^{20} \), then \( \frac{d^2y}{dx^2} = \):
If \( y = x^{20} \), then \( \frac{d^2y}{dx^2} = \):
Show Hint
To find the second derivative of a power function \( x^n \), apply the power rule twice:
\[
\frac{d^2}{dx^2} x^n = n(n - 1)x^{n - 2}
\]
Updated On: Nov 9, 2025
- \( x^{18} \)
- \( 20x^{19} \)
- \( 380x^{18} \)
- \( x^{19} \)
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The Correct Option is C
Solution and Explanation
Given:
\[
y = x^{20}
\]
First derivative:
\[
\frac{dy}{dx} = 20x^{19}
\]
Second derivative:
\[
\frac{d^2y}{dx^2} = \frac{d}{dx}(20x^{19}) = 20 \cdot 19 x^{18} = 380x^{18}
\]
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