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

The derivative of log_{e}(sqrt(x)) is 1/(2x)

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

The first derivative of log_{e}(sqrt(x)) is 1/(2x)

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

\frac{1}{2 x}

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{2 x}

\int \frac{9}{x ^{2} x ^{2} + 16} d x

tan^{2} (5 θ)

n = 1 \sum \infty 5 (- 1)^{n} n x^{n}

e^{- 4}

\frac{d}{d x} ((sin (x^{2}) + 1)^{\frac{1}{f ( x )}})

What is the derivative of log_{e}(sqrt(x)) ?
The derivative of log_{e}(sqrt(x)) is 1/(2x)
What is the first derivative of log_{e}(sqrt(x)) ?
The first derivative of log_{e}(sqrt(x)) is 1/(2x)