What is (\partial)/(\partial x)(x^2*e^x) ?

The answer to (\partial)/(\partial x)(x^2*e^x) is 2xe^x+e^xx^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(x^2*e^x)

\frac{\partial}{\partial x} (x^{2} \cdot e^{x})

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

Solution steps

\frac{\partial}{\partial x} (x^{2} e^{x})

Apply the Product Rule:

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

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

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

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

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

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

What is (\partial)/(\partial x)(x^2*e^x) ?
The answer to (\partial)/(\partial x)(x^2*e^x) is 2xe^x+e^xx^2