What is the derivative of (e^x/(4x^6)) ?

The derivative of (e^x/(4x^6)) is (e^x(x-6))/(4x^7)

What is the first derivative of (e^x/(4x^6)) ?

The first derivative of (e^x/(4x^6)) is (e^x(x-6))/(4x^7)

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}}{4 x ^{6}})

\frac{e ^{x} ( x - 6 )}{4 x ^{7}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{4 x ^{6}})

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (\frac{e ^{x}}{x ^{6}})

Apply the Quotient Rule:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( e ^{x} ) x ^{6} - \frac{d}{d x} ( x ^{6} ) e ^{x}}{( x ^{6} ) ^{2}}

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

\frac{d}{d x} (x^{6}) = 6 x^{5}

= \frac{1}{4} \cdot \frac{e ^{x} x ^{6} - 6 x ^{5} e ^{x}}{( x ^{6} ) ^{2}}

Simplify

\frac{1}{4} \cdot \frac{e ^{x} x ^{6} - 6 x ^{5} e ^{x}}{( x ^{6} ) ^{2}} : \frac{e ^{x} ( x - 6 )}{4 x ^{7}}

= \frac{e ^{x} ( x - 6 )}{4 x ^{7}}

\int \frac{5 x ^{2} + 7}{x ^{\frac{4}{3}}} d x

\int sin (π t) d t

\frac{d y}{d x} = \frac{x - 3}{y - 4}

\frac{\partial}{\partial x} ((2 x^{3} - 4 y) (2 x^{2} - 4))

\frac{d}{d x} (cos (\frac{π}{2}))

What is the derivative of (e^x/(4x^6)) ?
The derivative of (e^x/(4x^6)) is (e^x(x-6))/(4x^7)
What is the first derivative of (e^x/(4x^6)) ?
The first derivative of (e^x/(4x^6)) is (e^x(x-6))/(4x^7)