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

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

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

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

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Popular >

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

Expand

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

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

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

\frac{d}{d x} (e^{a x} sin (b x))

x^{2} \frac{d y}{d x} = 1 - x^{2} + y^{2} - x^{2} y^{2}

\int (x - a)^{2} d x

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

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