What is the derivative of (x-8/(5x^2e^x)) ?

The derivative of (x-8/(5x^2e^x)) is (-x^2+7x+16)/(5e^xx^3)

What is the first derivative of (x-8/(5x^2e^x)) ?

The first derivative of (x-8/(5x^2e^x)) is (-x^2+7x+16)/(5e^xx^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{x - 8}{5 x ^{2} e ^{x}})

\frac{- x ^{2} + 7 x + 16}{5 e ^{x} x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x - 8}{5 x ^{2} e ^{x}})

Take the constant out:

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

= \frac{1}{5} \frac{d}{d x} (\frac{x - 8}{x ^{2} e ^{x}})

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} ( x - 8 ) x ^{2} e ^{x} - \frac{d}{d x} ( x ^{2} e ^{x} ) ( x - 8 )}{( x ^{2} e ^{x} ) ^{2}}

\frac{d}{d x} (x - 8) = 1

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

= \frac{1}{5} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x - 8 )}{( x ^{2} e ^{x} ) ^{2}}

Simplify

\frac{1}{5} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x - 8 )}{( x ^{2} e ^{x} ) ^{2}} : \frac{- x ^{2} + 7 x + 16}{5 e ^{x} x ^{3}}

= \frac{- x ^{2} + 7 x + 16}{5 e ^{x} x ^{3}}

(2 x - 6)^{4} (x^{2} + x + 1)^{5}

\int \frac{10 x - 15}{x ^{2} + 25} d x

\int_{0}^{\frac{π}{9}} x tan^{2} (3 x) d x

\frac{d}{d x} (\frac{ln ( sin ( x ^{2} ) + 1 )}{f ( x )})

y = x^{2} - 2, (5, 23)

What is the derivative of (x-8/(5x^2e^x)) ?
The derivative of (x-8/(5x^2e^x)) is (-x^2+7x+16)/(5e^xx^3)
What is the first derivative of (x-8/(5x^2e^x)) ?
The first derivative of (x-8/(5x^2e^x)) is (-x^2+7x+16)/(5e^xx^3)