Find the second order derivative of the funct | vedclass

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Question

(A) Let $y = \log x$. First,we find the first order derivative with respect to $x$: $\frac{dy}{dx} = \frac{d}{dx}(\log x) = \frac{1}{x}$. Next,we find

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$-\frac{1}{x^{2}}$

Vedclass · Answer

(A) Let $y = \log x$. First,we find the first order derivative with respect to $x$: $\frac{dy}{dx} = \frac{d}{dx}(\log x) = \frac{1}{x}$. Next,we find the second order derivative by differentiating $\frac{dy}{dx}$ with respect to $x$: $\frac{d^{2}y}{dx^{2}} = \frac{d}{dx}\left(\frac{1}{x}\right) = \frac{d}{dx}(x^{-1}) = -1 \cdot x^{-2} = -\frac{1}{x^{2}}$. Thus,the second order derivative is $-\frac{1}{x^{2}}$.

Find the second order derivative of the function $f(x) = \log x$.

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