What is the derivative of (x/(y^2)-(y/(x^2))) ?

The derivative of (x/(y^2)-(y/(x^2))) is (y-2x\frac{dy)/(dx)}{y^3}-(x\frac{dy)/(dx)-2y}{x^3}

What is the first derivative of (x/(y^2)-(y/(x^2))) ?

The first derivative of (x/(y^2)-(y/(x^2))) is (y-2x\frac{dy)/(dx)}{y^3}-(x\frac{dy)/(dx)-2y}{x^3}

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

\frac{y - 2 x \frac{d y}{d x}}{y ^{3}} - \frac{x \frac{d y}{d x} - 2 y}{x ^{3}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{y - 2 x \frac{d y}{d x}}{y ^{3}} - \frac{x \frac{d y}{d x} - 2 y}{x ^{3}}

What is the derivative of (x/(y^2)-(y/(x^2))) ?
The derivative of (x/(y^2)-(y/(x^2))) is (y-2x\frac{dy)/(dx)}{y^3}-(x\frac{dy)/(dx)-2y}{x^3}
What is the first derivative of (x/(y^2)-(y/(x^2))) ?
The first derivative of (x/(y^2)-(y/(x^2))) is (y-2x\frac{dy)/(dx)}{y^3}-(x\frac{dy)/(dx)-2y}{x^3}