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

The derivative of (e^y/(x+y)) is (e^y\frac{dy)/(dx)(x+y)-(1+(dy)/(dx))e^y}{(x+y)^2}

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

The first derivative of (e^y/(x+y)) is (e^y\frac{dy)/(dx)(x+y)-(1+(dy)/(dx))e^y}{(x+y)^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{e ^{y}}{x + y})

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (e^{y}) = e^{y} \frac{d y}{d x}

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

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

\int (6 x^{2} cos (2 x^{3} + 1)) d x

\frac{d}{d x} (2 sin^{2} (x) + 5 sin (x) - 3)

\frac{d}{d x} (\frac{x}{e ^{2 x}})

y^{^{'}} + 8 x^{2} y = x^{2}

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

What is the derivative of (e^y/(x+y)) ?
The derivative of (e^y/(x+y)) is (e^y\frac{dy)/(dx)(x+y)-(1+(dy)/(dx))e^y}{(x+y)^2}
What is the first derivative of (e^y/(x+y)) ?
The first derivative of (e^y/(x+y)) is (e^y\frac{dy)/(dx)(x+y)-(1+(dy)/(dx))e^y}{(x+y)^2}