What is (\partial)/(\partial x)(1/((x-y)^2)) ?

The answer to (\partial)/(\partial x)(1/((x-y)^2)) is -2/((x-y)^3)

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(\partial)/(\partial x)(1/((x-y)^2))

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

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

Solution steps

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

Treat

y

as a constant

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{10 x ^{3} - 6 x ^{2} + 3}{4 x ^{2} - 6 x + 3}

x \to \infty lim (- \frac{1}{3} c e^{- 3 (x)})

\int (\frac{2}{x} - 4 e^{x}) d x

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

4 x, x^{2}

What is (\partial)/(\partial x)(1/((x-y)^2)) ?
The answer to (\partial)/(\partial x)(1/((x-y)^2)) is -2/((x-y)^3)