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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{x}{- x ^{2} + 4 x + 4} d x

x \to \infty lim (\frac{4 ^{x + 1} + 2 ^{x}}{4 ^{x}})

\frac{d}{d x} (- 7 ln (5 x^{2} - 11))

\int_{2}^{3} \frac{1}{- 7 + 16 x - 4 x ^{2}} d x

\int 1 0^{x^{2}} x d x

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