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

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

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

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

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

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

Take the constant out:

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

= 2 \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}}

= 2 \cdot \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}

= 2 \cdot \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}}

Simplify

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

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

x \to 45 lim (\frac{x ^{2}}{9} - \frac{5}{x})

\frac{d}{d x} (sin^{5} (2 x))

\frac{\partial}{\partial x} (x e^{x^{2}})

x y^{^{'}} - x^{2} y = - x^{2}

x^{2} - 3 x + 2

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