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

The answer to (\partial)/(\partial y)(((x^2))/((x-y)^2)) is (2x^2)/((x-y)^3)

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

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

\frac{2 x ^{2}}{( x - y ) ^{3}}

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{2}{( x - y ) ^{3}} \frac{\partial}{\partial y} (x - y)

= - \frac{2}{( x - y ) ^{3}} \frac{\partial}{\partial y} (x - y)

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

= x^{2} (- \frac{2}{( x - y ) ^{3}} (- 1))

Simplify

x^{2} (- \frac{2}{( x - y ) ^{3}} (- 1)) : \frac{2 x ^{2}}{( x - y ) ^{3}}

= \frac{2 x ^{2}}{( x - y ) ^{3}}

\frac{d y}{d x} = \frac{x - 3}{y + 1}

\int - \frac{x}{x ^{2} + 1} d x

\int \frac{1}{( x - 2 ) ^{2} ( x ^{2} - 4 x + 3 )} d x

f (x) = x^{3} + 4 x^{2} + 3 x

What is (\partial)/(\partial y)(((x^2))/((x-y)^2)) ?
The answer to (\partial)/(\partial y)(((x^2))/((x-y)^2)) is (2x^2)/((x-y)^3)