What is (\partial)/(\partial x)(sqrt(x^2y-xy^2)) ?

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

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(\partial)/(\partial x)(sqrt(x^2y-xy^2))

\frac{\partial}{\partial x} (x^{2} y - x y^{2})

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

Solution steps

\frac{\partial}{\partial x} (x^{2} y - x y^{2})

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 x ^{2} y - x y ^{2}} (2 y x - y^{2})

Simplify

\frac{1}{2 x ^{2} y - x y ^{2}} (2 y x - y^{2}) : \frac{2 x y - y ^{2}}{2 x ^{2} y - x y ^{2}}

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

\int x cos (2 x^{2}) d x

\int \frac{1 + e ^{x}}{e ^{x}} d x

y = \frac{1}{x - 5}, at x = 8

\frac{d}{d x} (cot (1 - 2 x^{2}))

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