What is (\partial)/(\partial x)(ln(4x)) ?

The answer to (\partial)/(\partial x)(ln(4x)) is 1/x

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(\partial)/(\partial x)(ln(4x))

\frac{\partial}{\partial x} (ln (4 x))

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (4 x))

Apply the chain rule:

\frac{1}{4 x} \frac{\partial}{\partial x} (4 x)

= \frac{1}{4 x} \frac{\partial}{\partial x} (4 x)

\frac{\partial}{\partial x} (4 x) = 4

= \frac{1}{4 x} \cdot 4

Simplify

\frac{1}{4 x} \cdot 4 : \frac{1}{x}

= \frac{1}{x}

y = 5 x^{2} - 10 x - 6 x^{- 2}

\frac{d}{d x} (\frac{sin ( x )}{cos ( x )})

\frac{\partial}{\partial x} (- \frac{x - y}{x ^{2} ( x + y )})

f (x) = 2 (13 - x^{4})

\int_{1}^{8} \frac{1}{x 16 x ^{2} - 9} d x

What is (\partial)/(\partial x)(ln(4x)) ?
The answer to (\partial)/(\partial x)(ln(4x)) is 1/x