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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (2 x lo g_{10} (x))

t \frac{d Q}{d t} + Q = t^{5} ln (t)

\int \frac{3}{1 + 2 e ^{x} - e ^{- x}} d x

t \to - 1 lim (t^{2} - x^{2})

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