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

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

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

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

\frac{1}{y ^{2}} + \frac{2 y}{x ^{3}}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

= \frac{1}{y ^{2}} + \frac{2 y}{x ^{3}}

(x^{2})^{- 1}

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

\int \frac{1}{x ( 10 - x )} d x

\frac{\partial}{\partial x} (\frac{x + 2}{y + 1})

\frac{d}{d x} (x e^{9 x})

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