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

The derivative of (e^{2x}/(x^2)) is (2e^{2x}(x-1))/(x^3)

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

The first derivative of (e^{2x}/(x^2)) is (2e^{2x}(x-1))/(x^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 ^{2 x}}{x ^{2}})

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int x^{2} - 7 x + 6 d x

\frac{d}{d x} (2 \cdot sin (x) \cdot cos (x))

\int 1 + x^{\frac{1}{2}} d x

\frac{d}{d x} (x + b)

\int \frac{1}{x ^{2} + 6} d x

What is the derivative of (e^{2x}/(x^2)) ?
The derivative of (e^{2x}/(x^2)) is (2e^{2x}(x-1))/(x^3)
What is the first derivative of (e^{2x}/(x^2)) ?
The first derivative of (e^{2x}/(x^2)) is (2e^{2x}(x-1))/(x^3)