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The differentiate of $\\ln(x)$ is $\\frac{1}{x}$.

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This proof can be found here.

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For natural logarithms in the form $u\\ln(a(x))$ where $a(x)$ is a function of $x$, the derivative is $u\\frac{a'(x)}{a(x)}$.

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$y=\\ln(x)$

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$\\frac{dy}{dx}=$ [[0]]

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$y=-\\ln(\\var{c[0]}x)$

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$\\frac{dy}{dx}=$ [[0]]

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$y=\\var{c[1]}\\ln(\\var{c[2]}x)$

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$\\frac{dy}{dx}=$ [[0]]

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$y=\\ln(x^\\var{p}+\\var{c[3]})$

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$\\frac{dy}{dx}=$ [[0]]

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$y=\\ln(\\var{c[3]}x^2+\\var{c[4]}x+\\var{c[5]})$

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$\\frac{dy}{dx}=$ [[0]]

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Differentiate the following.

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Do not write out $dy/dx$; only input the differentiated right hand side of each equation.

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Differentiating the natural logarithm

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