What is (\partial)/(\partial x)((3xy)/(x^2+y^2)) ?

The answer to (\partial)/(\partial x)((3xy)/(x^2+y^2)) is (3y(-x^2+y^2))/((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 >

(\partial)/(\partial x)((3xy)/(x^2+y^2))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

= 3 y \frac{1 \cdot ( x ^{2} + y ^{2} ) - 2 xx}{( x ^{2} + y ^{2} ) ^{2}}

Simplify

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

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

\int ln (2) d x

e^{- 7 x}, 0

\int arctan^{2} (x) d x

\frac{d}{d x} (cos^{4} (x) + sin^{4} (x))

x \to 3 + lim (\frac{3}{x - 3})

What is (\partial)/(\partial x)((3xy)/(x^2+y^2)) ?
The answer to (\partial)/(\partial x)((3xy)/(x^2+y^2)) is (3y(-x^2+y^2))/((x^2+y^2)^2)