What is the derivative of (e^x/(5x^2)) ?

The derivative of (e^x/(5x^2)) is (e^x(x-2))/(5x^3)

What is the first derivative of (e^x/(5x^2)) ?

The first derivative of (e^x/(5x^2)) is (e^x(x-2))/(5x^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}}{5 x ^{2}})

\frac{e ^{x} ( x - 2 )}{5 x ^{3}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2}})

Take the constant out:

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

= \frac{1}{5} \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}{5} \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}{5} \cdot \frac{e ^{x} x ^{2} - 2 x e ^{x}}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{5} \cdot \frac{e ^{x} x ^{2} - 2 x e ^{x}}{( x ^{2} ) ^{2}} : \frac{e ^{x} ( x - 2 )}{5 x ^{3}}

= \frac{e ^{x} ( x - 2 )}{5 x ^{3}}

\frac{d}{d x} (e^{x} sin (x) + cos (x) e^{x})

\frac{d}{d x} (\frac{- 6 x}{( x ^{2} - 4 ) ^{2}})

\int e^{x^{0.5}} d x

\frac{\partial}{\partial x} (a x^{b} y^{(1 - b)})

\frac{d y}{d x} = (- 10 x^{4} y)

What is the derivative of (e^x/(5x^2)) ?
The derivative of (e^x/(5x^2)) is (e^x(x-2))/(5x^3)
What is the first derivative of (e^x/(5x^2)) ?
The first derivative of (e^x/(5x^2)) is (e^x(x-2))/(5x^3)