en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^7e^{4x}

Solution

\frac{d}{d x} (x^{7} e^{4 x})

Solution

7 x^{6} e^{4 x} + e^{4 x} \cdot 4 x^{7}

Solution steps

\frac{d}{d x} (x^{7} e^{4 x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{7}, g = e^{4 x}

= \frac{d}{d x} (x^{7}) e^{4 x} + \frac{d}{d x} (e^{4 x}) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

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

= 7 x^{6} e^{4 x} + e^{4 x} \cdot 4 x^{7}

Graph

Popular Examples

integral of x^5sin(x^6)

\int x^{5} sin (x^{6}) d x

derivative of 3/(((56(2x-1)^7))-1/(((24)(2x-1)^6))-1/(((40(2x-1)^5))))

\frac{d}{d x} \frac{3}{( ( 56 ) ( 2 x - 1 ) ^{7} )} - \frac{1}{( ( 24 ) ( 2 x - 1 ) ^{6} )} - \frac{1}{( ( 40 ( 2 x - 1 ) ^{5} ) )}

derivative of 1/(x+y^2)

\frac{d}{d x} (\frac{1}{x + y ^{2}})

y^{^{'}} = 2 x + 3 y - 1

derivative of 1/(sqrt(2x+1))

\frac{d}{d x} (\frac{1}{2 x + 1})

Frequently Asked Questions (FAQ)

What is the derivative of x^7e^{4x} ?
The derivative of x^7e^{4x} is 7x^6e^{4x}+e^{4x}*4x^7
What is the first derivative of x^7e^{4x} ?
The first derivative of x^7e^{4x} is 7x^6e^{4x}+e^{4x}*4x^7