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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

n = 0 \sum \infty \frac{4}{5 ^{n - 1}}

x \to - 2 - lim (\frac{x}{x + 2})

\int \frac{1}{( e ^{x} - 3 ) ^{2}} d x

x \to 64 lim (x^{\frac{2}{3}})

e^{- t} \cdot sin (t)

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