What is (\partial)/(\partial x)(ln(sqrt(x))) ?

The answer to (\partial)/(\partial x)(ln(sqrt(x))) is 1/(2x)

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(\partial)/(\partial x)(ln(sqrt(x)))

\frac{\partial}{\partial x} (ln (x))

\frac{1}{2 x}

Solution steps

\frac{\partial}{\partial x} (ln (x))

Apply the chain rule:

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

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

\frac{\partial}{\partial 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}

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{e ^{x}})

\frac{d y}{d x} = x^{4} y^{- 5}

y = 3 x e^{- k x}

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

\int - \frac{3}{25} x + 49 d x

What is (\partial)/(\partial x)(ln(sqrt(x))) ?
The answer to (\partial)/(\partial x)(ln(sqrt(x))) is 1/(2x)