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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

Simplify

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

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

n = 0 \sum \infty e^{2}

\frac{d}{d x} (d - a x - b - \frac{d}{x ^{2}})

f (x) = tan (x), at x = \frac{π}{4}

f (x) = \frac{2 - 3 x - x ^{2}}{x ^{2} - 5}

\int x^{e} + \frac{2}{x} + sec^{2} (2 x) d x

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