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

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

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

\frac{\partial}{\partial x} (x \cdot y - x \cdot 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} (cos (x^{2} + 1))

\int \frac{x}{x ^{2} + 6} d x

\int 10 x^{2} d x

\int e^{7 x} sin (5 x) d x

\frac{d y}{d x} = - \frac{y ^{2}}{1 + y ^{2}} \cdot e^{- x}

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