What is (\partial)/(\partial x)(ln(9x)) ?

The answer to (\partial)/(\partial x)(ln(9x)) is 1/x

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(\partial)/(\partial x)(ln(9x))

\frac{\partial}{\partial x} (ln (9 x))

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (9 x))

Apply the chain rule:

\frac{1}{9 x} \frac{\partial}{\partial x} (9 x)

= \frac{1}{9 x} \frac{\partial}{\partial x} (9 x)

\frac{\partial}{\partial x} (9 x) = 9

= \frac{1}{9 x} \cdot 9

Simplify

\frac{1}{9 x} \cdot 9 : \frac{1}{x}

= \frac{1}{x}

What is (\partial)/(\partial x)(ln(9x)) ?
The answer to (\partial)/(\partial x)(ln(9x)) is 1/x