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

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

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

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

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{x - y}{x + y})

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

Solution steps

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

Apply the chain rule:

\frac{1}{2 \frac{x - y}{x + y}} \frac{d}{d x} (\frac{x - y}{x + y})

= \frac{1}{2 \frac{x - y}{x + y}} \frac{d}{d x} (\frac{x - y}{x + y})

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

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

Simplify

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

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

e^{- 0.5 \cdot 10}

5 1.2454 5^{^{'}}

x (2 x y e^{x y^{2}})

(2.3 \cdot 1 0^{- 19}) \cdot 0.28

16 e^{- 0.000121 (8967)}

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