Question

If \( y = x^{20} \), then \( \frac{d^2y}{dx^2} = \):

• A. \( x^{18} \)
• B. \( 20x^{19} \)
• C. \( 380x^{18} \)
• D. \( x^{19} \)

Hint:

To find the second derivative of a power function \( x^n \), apply the power rule twice: \[ \frac{d^2}{dx^2} x^n = n(n - 1)x^{n - 2} \]

Answer 1

The Correct Option is C

Given: \[ y = x^{20} \] First derivative: \[ \frac{dy}{dx} = 20x^{19} \] Second derivative: \[ \frac{d^2y}{dx^2} = \frac{d}{dx}(20x^{19}) = 20 \cdot 19 x^{18} = 380x^{18} \]