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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

4 y^{^{''}} - 12 y^{^{'}} + 9 y = 0, y (0) = 3, y^{^{'}} (0) = 5

n \to \infty lim (\frac{ln ( n )}{ln ( 2 n )})

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

x \to 0 lim (x^{0})

f (x) = \frac{1}{x - 3}

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