en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of 6x^5e^{6x}

Solution

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

Solution

6 (5 x^{4} e^{6 x} + e^{6 x} \cdot 6 x^{5})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{5}, g = e^{6 x}

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 6 (5 x^{4} e^{6 x} + e^{6 x} \cdot 6 x^{5})

Graph

Popular Examples

derivative of (1-2x/(6+x))

\frac{d}{d x} (\frac{1 - 2 x}{6 + x})

tangent of f(x)=4x-3sqrt(x)

t an g e n t f (x) = 4 x - 3 x

derivative of ax^n

\frac{d}{d x} (a x^{n})

sum from k=1 to infinity of (k!)/(2^k)

k = 1 \sum \infty \frac{k !}{2 ^{k}}

integral of 15tan^2(x)sec^3(x)

\int 15 tan^{2} (x) sec^{3} (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of 6x^5e^{6x} ?
The derivative of 6x^5e^{6x} is 6(5x^4e^{6x}+e^{6x}*6x^5)
What is the first derivative of 6x^5e^{6x} ?
The first derivative of 6x^5e^{6x} is 6(5x^4e^{6x}+e^{6x}*6x^5)