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Differentiating the natural logarithm

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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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For example  $-\\frac{3}{4}x^2+\\frac{5}{6}x^{-\\frac{4}{5}}-12x+4x^3e^{(2x^2-2)}$

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Would be entered -(3/4)*x^2   +(5/6)*x^(-4/5)   -12*x   + 4*x^3*e^(2x^2-2)

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

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$\\frac{dy}{dx}=$ [[0]]

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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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