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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int e^{x + 9 e^{x}} d x

y = 2 x^{\frac{1}{3}}, 0 \leq x \leq 32

4 (3 x + y - 2) d x - (3 x + y) d y = 0

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

y^{^{'}} = \frac{- y}{40 - t}

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