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

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

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

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

\frac{y}{2 x} - y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{y}{2 x} - y

\frac{d}{d x} (e^{x} sin (x) + e^{x} cos (x))

\int \frac{x ^{3}}{( 1 - x ^{4} ) ^{6}} d x

\frac{d}{d x} (x^{2} e^{x} - 2 x e^{x} + 8 e^{x})

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

x \to 0 lim (\frac{6 ^{x} - 1}{x})

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