What is the derivative of x^2e^{3x} ?

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

What is the first derivative of x^2e^{3x} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

x^{2} e^{3 x}

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

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = e^{3 x}

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

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

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

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

x

f (x) = 3 x + 8, at x = 4

(8.4) (20.1)

y = 2 x + 3

x^{2} + y^{2} + 2 x y = 4, (1, 1)

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