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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{''}} - 5 y^{^{'}} + 4 y = 8 e^{x}

\int_{- 2}^{2} x d x

f (x) = - x^{2} + 16 x + 63, at x = 2

\int ln (4 x) d x

\int_{1}^{12} (0.5)^{x} d x

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