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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{x - 2}{3 x ^{2} e ^{x}}

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x - 2) = 1

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

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

Simplify

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

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

\frac{\partial}{\partial x} (3 x + 4 t)

f (x) = sin (3 ln (x))

y = 11 x + 11 x + 11 x

x^{2} + x

(x + 1)^{3} (x - 1)

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