What is the derivative of (e^{4x^2}/(x^2)) ?

The derivative of (e^{4x^2}/(x^2)) is (2e^{4x^2}(4x^2-1))/(x^3)

What is the first derivative of (e^{4x^2}/(x^2)) ?

The first derivative of (e^{4x^2}/(x^2)) is (2e^{4x^2}(4x^2-1))/(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 ^{4 x^{2}}}{x ^{2}})

\frac{2 e ^{4 x^{2}} ( 4 x ^{2} - 1 )}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{e ^{4 x^{2}}}{x ^{2}})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (e^{4 x^{2}}) = e^{4 x^{2}} \cdot 8 x

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

= \frac{e ^{4 x^{2}} \cdot 8 x x ^{2} - 2 x e ^{4 x^{2}}}{( x ^{2} ) ^{2}}

Simplify

\frac{e ^{4 x^{2}} \cdot 8 x x ^{2} - 2 x e ^{4 x^{2}}}{( x ^{2} ) ^{2}} : \frac{2 e ^{4 x^{2}} ( 4 x ^{2} - 1 )}{x ^{3}}

= \frac{2 e ^{4 x^{2}} ( 4 x ^{2} - 1 )}{x ^{3}}

x^{2} - 10, 9 x

\int \frac{1}{e ^{2 x} - 4} d x

\int x^{2} ln (4 x) d x

x \to - \frac{π}{4} lim (sec (x))

x \to 1 lim (+ (\frac{1}{x ^{2} - 1}))

What is the derivative of (e^{4x^2}/(x^2)) ?
The derivative of (e^{4x^2}/(x^2)) is (2e^{4x^2}(4x^2-1))/(x^3)
What is the first derivative of (e^{4x^2}/(x^2)) ?
The first derivative of (e^{4x^2}/(x^2)) is (2e^{4x^2}(4x^2-1))/(x^3)