What is (\partial)/(\partial x)(ln(2x)) ?

The answer to (\partial)/(\partial x)(ln(2x)) is 1/x

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(\partial)/(\partial x)(ln(2x))

\frac{\partial}{\partial x} (ln (2 x))

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (2 x))

Apply the chain rule:

\frac{1}{2 x} \frac{\partial}{\partial x} (2 x)

= \frac{1}{2 x} \frac{\partial}{\partial x} (2 x)

\frac{\partial}{\partial x} (2 x) = 2

= \frac{1}{2 x} \cdot 2

Simplify

\frac{1}{2 x} \cdot 2 : \frac{1}{x}

= \frac{1}{x}

y^{^{'}} - \frac{9}{x} y = \frac{y ^{4}}{x ^{12}}

\frac{d y}{d t} = - y^{2} t - y^{2} t^{2}

\frac{d ^{2} y}{d x ^{2}} + \frac{2}{x} \frac{d y}{d x} = 3 x + 4

x \to 2 - lim (2 - \frac{1}{x - 2})

\frac{d y}{d x} = \frac{4 x ^{2} + 2 x}{y ^{2}}

What is (\partial)/(\partial x)(ln(2x)) ?
The answer to (\partial)/(\partial x)(ln(2x)) is 1/x