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}}

\int - \frac{1}{x} d x

\frac{d}{d x} (ln (x^{13}))

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

\int 3 y^{2} (e^{y^{3}} - 1) d y

n = 1001 \sum \infty \frac{1}{n}

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)