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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 2 \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}}

= 2 \cdot \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

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

Simplify

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

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

(2 x + 5) (5 x^{2} + 1)

\int_{0}^{\frac{3 π}{2}} 7 ∣ sin (x) ∣ d x

f (x) = e^{x}, g (x) = cos (x), x = 0, x = \frac{π}{2}

y = x^{2} - 3 x, y = x

\int_{0}^{2} x (1 - x) d x

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