What is the derivative of x^3e^{5x} ?

The derivative of x^3e^{5x} is 3x^2e^{5x}+e^{5x}*5x^3

What is the first derivative of x^3e^{5x} ?

The first derivative of x^3e^{5x} is 3x^2e^{5x}+e^{5x}*5x^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} (x^{3} e^{5 x})

3 x^{2} e^{5 x} + e^{5 x} \cdot 5 x^{3}

Solution steps

\frac{d}{d x} (x^{3} e^{5 x})

Apply the Product Rule:

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

f = x^{3}, g = e^{5 x}

= \frac{d}{d x} (x^{3}) e^{5 x} + \frac{d}{d x} (e^{5 x}) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} e^{5 x} + e^{5 x} \cdot 5 x^{3}

\int (x + \frac{1}{6 x}) d x

\int_{0}^{1} x (x^{2} - x) d x

\int \frac{x}{y} d y

n = 0 \sum \infty \frac{- 1 ^{n}}{n !}

y = x^{10} + 1 + 1 - x

What is the derivative of x^3e^{5x} ?
The derivative of x^3e^{5x} is 3x^2e^{5x}+e^{5x}*5x^3
What is the first derivative of x^3e^{5x} ?
The first derivative of x^3e^{5x} is 3x^2e^{5x}+e^{5x}*5x^3