What is the derivative of f(x)=(e^x)/(x+3) ?

The derivative of f(x)=(e^x)/(x+3) is (e^xx+2e^x)/((x+3)^2)

What is the first derivative of f(x)=(e^x)/(x+3) ?

The first derivative of f(x)=(e^x)/(x+3) is (e^xx+2e^x)/((x+3)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{e ^{x}}{x + 3}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x + 3) = 1

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

Simplify

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

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

\frac{( s + 5 )}{( s ^{2} + 4 s + 13 )}

\frac{d}{d x} (x^{2} (1 - x)^{3})

\int \frac{( tan ^{3} ( ln ( x ) ) )}{6 x} d x

9 y^{^{''}} + 10 y = 0

\frac{\partial}{\partial v} (u)

What is the derivative of f(x)=(e^x)/(x+3) ?
The derivative of f(x)=(e^x)/(x+3) is (e^xx+2e^x)/((x+3)^2)
What is the first derivative of f(x)=(e^x)/(x+3) ?
The first derivative of f(x)=(e^x)/(x+3) is (e^xx+2e^x)/((x+3)^2)