What is (\partial)/(\partial x)(ln(x/3)) ?

The answer to (\partial)/(\partial x)(ln(x/3)) is 1/x

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(\partial)/(\partial x)(ln(x/3))

\frac{\partial}{\partial x} (ln (\frac{x}{3}))

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (\frac{x}{3}))

Apply the chain rule:

\frac{1}{\frac{x}{3}} \frac{\partial}{\partial x} (\frac{x}{3})

= \frac{1}{\frac{x}{3}} \frac{\partial}{\partial x} (\frac{x}{3})

\frac{\partial}{\partial x} (\frac{x}{3}) = \frac{1}{3}

= \frac{1}{\frac{x}{3}} \cdot \frac{1}{3}

Simplify

\frac{1}{\frac{x}{3}} \cdot \frac{1}{3} : \frac{1}{x}

= \frac{1}{x}

n = 1 \sum \infty n^{2} e^{- n}

x \to 2 lim (\frac{x + 3}{x + 6})

\int e^{x} cosh (x) d x

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\int - \frac{1}{( t + 2 ) ^{2}} d t

What is (\partial)/(\partial x)(ln(x/3)) ?
The answer to (\partial)/(\partial x)(ln(x/3)) is 1/x