What is (\partial)/(\partial x)(log_{10}(2x)) ?

The answer to (\partial)/(\partial x)(log_{10}(2x)) is 1/(ln(10)x)

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(\partial)/(\partial x)(log_{10}(2x))

\frac{\partial}{\partial x} (lo g_{10} (2 x))

\frac{1}{ln ( 10 ) x}

Solution steps

\frac{\partial}{\partial x} (lo g_{10} (2 x))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{\partial}{\partial x} (\frac{ln ( 2 x )}{ln ( 10 )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 10 )} \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}{ln ( 10 )} \cdot \frac{1}{2 x} \cdot 2

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{2 x} \cdot 2 : \frac{1}{ln ( 10 ) x}

= \frac{1}{ln ( 10 ) x}

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What is (\partial)/(\partial x)(log_{10}(2x)) ?
The answer to (\partial)/(\partial x)(log_{10}(2x)) is 1/(ln(10)x)