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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

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

x \to π - lim (cot (x))

8 e^{4 x}

x y - 5 y^{2} = 4

4 t e^{3 t} sin (2 t)

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