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

The derivative of x/((x^2+y^2^2)) is (y^2-3x^2-4x\frac{dy)/(dx)y}{(x^2+y^2)^3}

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

The first derivative of x/((x^2+y^2^2)) is (y^2-3x^2-4x\frac{dy)/(dx)y}{(x^2+y^2)^3}

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

\frac{y ^{2} - 3 x ^{2} - 4 x \frac{d y}{d x} y}{( x ^{2} + y ^{2} ) ^{3}}

Solution steps

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

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

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

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

Simplify

\frac{1 \cdot ( x ^{2} + y ^{2} ) ^{2} - 2 ( x ^{2} + y ^{2} ) ( 2 x + 2 y \frac{d y}{d x} ) x}{( ( x ^{2} + y ^{2} ) ^{2} ) ^{2}} : \frac{y ^{2} - 3 x ^{2} - 4 x \frac{d y}{d x} y}{( x ^{2} + y ^{2} ) ^{3}}

= \frac{y ^{2} - 3 x ^{2} - 4 x \frac{d y}{d x} y}{( x ^{2} + y ^{2} ) ^{3}}

\frac{d}{d t} (\frac{2}{t ^{2} + 2})

\int \frac{1}{- u ^{2} - a + b} d u

\frac{d}{d t} (tan (e^{6 t}) + e^{t a n (6 t)})

\frac{\partial}{\partial x} (cos (x y) + e^{yz} + ln (z x))

f^{9}

What is the derivative of x/((x^2+y^2^2)) ?
The derivative of x/((x^2+y^2^2)) is (y^2-3x^2-4x\frac{dy)/(dx)y}{(x^2+y^2)^3}
What is the first derivative of x/((x^2+y^2^2)) ?
The first derivative of x/((x^2+y^2^2)) is (y^2-3x^2-4x\frac{dy)/(dx)y}{(x^2+y^2)^3}