What is the derivative of (x^2+2xe^x) ?

The derivative of (x^2+2xe^x) is e^xx^2+4e^xx+2e^x

What is the first derivative of (x^2+2xe^x) ?

The first derivative of (x^2+2xe^x) is e^xx^2+4e^xx+2e^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

e^{x} x^{2} + 4 e^{x} x + 2 e^{x}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(2 x + 2) e^{x} + e^{x} (x^{2} + 2 x) : e^{x} x^{2} + 4 e^{x} x + 2 e^{x}

= e^{x} x^{2} + 4 e^{x} x + 2 e^{x}

What is the derivative of (x^2+2xe^x) ?
The derivative of (x^2+2xe^x) is e^xx^2+4e^xx+2e^x
What is the first derivative of (x^2+2xe^x) ?
The first derivative of (x^2+2xe^x) is e^xx^2+4e^xx+2e^x