What is the derivative of (e^x/(7x^2)) ?

The derivative of (e^x/(7x^2)) is (e^x(x-2))/(7x^3)

What is the first derivative of (e^x/(7x^2)) ?

The first derivative of (e^x/(7x^2)) is (e^x(x-2))/(7x^3)

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 ^{x}}{7 x ^{2}})

\frac{e ^{x} ( x - 2 )}{7 x ^{3}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{2}})

Take the constant out:

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

= \frac{1}{7} \frac{d}{d x} (\frac{e ^{x}}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{1}{7} \cdot \frac{\frac{d}{d x} ( e ^{x} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) e ^{x}}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{7} \cdot \frac{e ^{x} x ^{2} - 2 x e ^{x}}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{7} \cdot \frac{e ^{x} x ^{2} - 2 x e ^{x}}{( x ^{2} ) ^{2}} : \frac{e ^{x} ( x - 2 )}{7 x ^{3}}

= \frac{e ^{x} ( x - 2 )}{7 x ^{3}}

sin (x), 5 x, \frac{π}{2}, π

x \to - 2 lim (x + 3)

f (x) = (x^{2} - 5) e^{x}

\frac{\partial}{\partial y} (1)

\frac{d x}{d t} = 5 x (8 - x)

What is the derivative of (e^x/(7x^2)) ?
The derivative of (e^x/(7x^2)) is (e^x(x-2))/(7x^3)
What is the first derivative of (e^x/(7x^2)) ?
The first derivative of (e^x/(7x^2)) is (e^x(x-2))/(7x^3)