What is (\partial)/(\partial x)(y-ln(sqrt(xy))) ?

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

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(\partial)/(\partial x)(y-ln(sqrt(xy)))

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

- \frac{1}{2 x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (y) = 0

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

= 0 - \frac{1}{2 x}

Simplify

= - \frac{1}{2 x}

\frac{d ^{2}}{d x ^{2}} ((14 t^{2} + 6)^{0.5})

10 x^{^{''}} + 1000 x = 0

\frac{d}{d x} (\frac{4 π x ^{3}}{3})

(e^{x} + e^{- x})^{^{'}}

x (x + 1) y^{^{'}} + x y = 1, y (e) = 1

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