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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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