What is the derivative of log_{e}(5x) ?

The derivative of log_{e}(5x) is 1/x

What is the first derivative of log_{e}(5x) ?

The first derivative of log_{e}(5x) is 1/x

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\frac{d}{d x} (lo g_{e} (5 x))

\frac{1}{x}

Solution steps

\frac{d}{d x} (lo g_{e} (5 x))

Simplify

lo g_{e} (5 x) : ln (5 x)

= \frac{d}{d x} (ln (5 x))

Apply the chain rule:

\frac{1}{5 x} \frac{d}{d x} (5 x)

= \frac{1}{5 x} \frac{d}{d x} (5 x)

\frac{d}{d x} (5 x) = 5

= \frac{1}{5 x} \cdot 5

Simplify

\frac{1}{5 x} \cdot 5 : \frac{1}{x}

= \frac{1}{x}

\int \frac{x ^{2}}{8 - x ^{3}} d x

\frac{d}{d t} (\frac{1}{2 + t})

\frac{d}{d z} (\frac{z}{z + \frac{a}{z}})

y^{^{''}} + 2 y^{^{'}} = 8 x

What is the derivative of log_{e}(5x) ?
The derivative of log_{e}(5x) is 1/x
What is the first derivative of log_{e}(5x) ?
The first derivative of log_{e}(5x) is 1/x