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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

Expand

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

\frac{d}{d x} (cos^{4} (x) - 2 x^{2})

\frac{1}{s + 11}

\frac{d y}{d t} + t y = y

(- 3, 1), (2, - 14)

\frac{\partial}{\partial y} (2 x y - sec^{2} (x))

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