What is the derivative of (2xy/((2-x^2))) ?

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

What is the first derivative of (2xy/((2-x^2))) ?

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

cos (6 y)

\frac{d}{d x} (\frac{a x + b}{c x + d})

x \to 1 lim (arccos (x))

\frac{d}{d s} (\frac{6}{s ^{2} + 36})

\frac{d ^{2}}{d x ^{2}} (x^{2} + 16)

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