What is the derivative of ln(sqrt(2x)) ?

The derivative of ln(sqrt(2x)) is 1/(2x)

What is the first derivative of ln(sqrt(2x)) ?

The first derivative of ln(sqrt(2x)) is 1/(2x)

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\frac{d}{d x} (ln (2 x))

\frac{1}{2 x}

Solution steps

\frac{d}{d x} (ln (2 x))

Simplify

ln (2 x) : ln (2 x)

= \frac{d}{d x} (ln (2 x))

Apply the chain rule:

\frac{1}{2 x} \frac{d}{d x} (2 x)

= \frac{1}{2 x} \frac{d}{d x} (2 x)

\frac{d}{d x} (2 x) = \frac{1}{2 x}

= \frac{1}{2 x} \cdot \frac{1}{2 x}

Simplify

\frac{1}{2 x} \cdot \frac{1}{2 x} : \frac{1}{2 x}

= \frac{1}{2 x}

\int \frac{8}{x + 1} d x

\frac{\partial}{\partial x} (\frac{5}{5 x + 3 y})

\frac{10}{s ( s + 2 ) ( s + 3 ) ^{2}}

x \to 0 - lim (x sin (\frac{1}{x}))

x y^{^{'}} + y = - 5 x y^{2}, y (1) = 7

What is the derivative of ln(sqrt(2x)) ?
The derivative of ln(sqrt(2x)) is 1/(2x)
What is the first derivative of ln(sqrt(2x)) ?
The first derivative of ln(sqrt(2x)) is 1/(2x)