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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Expand

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

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

f (x) = 5 x^{3} - 5 x, at x = - 1

\frac{d}{d x} (cos^{n - 1} (x))

y = x^{4} - 4 x^{3} + 10

2 x, x ∣ x + 2 ∣

\frac{d y}{d x} + 3 y = 10, y (0) = 20

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