What is the derivative of log_{e}(4x) ?

The derivative of log_{e}(4x) is 1/x

What is the first derivative of log_{e}(4x) ?

The first derivative of log_{e}(4x) is 1/x

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\frac{d}{d x} (lo g_{e} (4 x))

\frac{1}{x}

Solution steps

\frac{d}{d x} (lo g_{e} (4 x))

Simplify

lo g_{e} (4 x) : ln (4 x)

= \frac{d}{d x} (ln (4 x))

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x}

\frac{d}{d x} ((8 (4 x)^{4} + 5)^{3})

\frac{\partial}{\partial y} (arctan (x) y)

4 - ln (x)

y^{^{''}} + 4 y^{^{'}} + 40 y = 40 cos (8 t)

\frac{\partial}{\partial x} (\frac{1}{3 x})

What is the derivative of log_{e}(4x) ?
The derivative of log_{e}(4x) is 1/x
What is the first derivative of log_{e}(4x) ?
The first derivative of log_{e}(4x) is 1/x