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}}

f (x) = \frac{1}{1 + x ^{2}}, at x = - 1

\frac{\partial}{\partial θ} (n ln (2 θ))

\int \frac{50 x}{sec ( 5 x ^{2} + 5 )} d x

x \to 0 lim (\frac{( 8 ^{x} - 5 ^{x} )}{x})

\frac{1}{e ^{x^{2}}}

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}