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

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

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(\partial)/(\partial x)(ln(ysqrt(x)))

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

\frac{1}{2 x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (y x) = \frac{y}{2 x}

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

Simplify

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

= \frac{1}{2 x}

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