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

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

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

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

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

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

Solution steps

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

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

Simplify

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

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

7 \frac{7}{15} - 4 \frac{9}{4} - 5 \frac{4}{6}

\frac{\frac{3}{5}}{- \frac{4}{5}}

(- 2 - 5 i)^{2}

\frac{6 x ^{3} + 11 x ^{2} + 9 x + 2}{3 x + 1}

lo g_{3} (75)

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