en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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})

Popular Examples

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

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

integral of (x^3)/(2x^2-x-1)

\int \frac{x ^{3}}{2 x ^{2} - x - 1} d x

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

f (x) = 4 x - 3 x

derivative of ax^n

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

derivative of 1/(sqrt(x^4+1))

\frac{d}{d x} (\frac{1}{x ^{4} + 1})

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)