What is the derivative of 3x^2e^x+x^3e^x ?

The derivative of 3x^2e^x+x^3e^x is 6e^xx+6e^xx^2+e^xx^3

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

The first derivative of 3x^2e^x+x^3e^x is 6e^xx+6e^xx^2+e^xx^3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

6 e^{x} x + 6 e^{x} x^{2} + e^{x} x^{3}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= 3 (2 x e^{x} + e^{x} x^{2}) + 3 x^{2} e^{x} + e^{x} x^{3}

Simplify

3 (2 x e^{x} + e^{x} x^{2}) + 3 x^{2} e^{x} + e^{x} x^{3} : 6 e^{x} x + 6 e^{x} x^{2} + e^{x} x^{3}

= 6 e^{x} x + 6 e^{x} x^{2} + e^{x} x^{3}

What is the derivative of 3x^2e^x+x^3e^x ?
The derivative of 3x^2e^x+x^3e^x is 6e^xx+6e^xx^2+e^xx^3
What is the first derivative of 3x^2e^x+x^3e^x ?
The first derivative of 3x^2e^x+x^3e^x is 6e^xx+6e^xx^2+e^xx^3