Find the second order derivative of the funct | vedclass

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Question

(A) Let $y = x^{20}$.First,find the first order derivative with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx}(x^{20}) = 20x^{19}$.Next,find the second

Vedclass · Accepted Answer

$380 x^{18}$

Vedclass · Answer

(A) Let $y = x^{20}$.First,find the first order derivative with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx}(x^{20}) = 20x^{19}$.Next,find the second order derivative by differentiating the first derivative with respect to $x$:$\frac{d^2y}{dx^2} = \frac{d}{dx}(20x^{19}) = 20 \cdot \frac{d}{dx}(x^{19})$.Using the power rule $\frac{d}{dx}(x^n) = nx^{n-1}$:$\frac{d^2y}{dx^2} = 20 \cdot 19x^{18} = 380x^{18}$.

Find the second order derivative of the function $f(x) = x^{20}$.

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