What is the derivative of 9(2xe^x+e^xx^2) ?

The derivative of 9(2xe^x+e^xx^2) is 9(e^xx^2+4e^xx+2e^x)

What is the first derivative of 9(2xe^x+e^xx^2) ?

The first derivative of 9(2xe^x+e^xx^2) is 9(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

Popular >

\frac{d}{d x} (9 (2 x e^{x} + e^{x} x^{2}))

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

Solution steps

\frac{d}{d x} (9 (2 x e^{x} + e^{x} x^{2}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{d}{d x} (2 x e^{x} + e^{x} x^{2})

Apply the Sum/Difference Rule:

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

= 9 (\frac{d}{d x} (2 x e^{x}) + \frac{d}{d x} (e^{x} x^{2}))

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

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

= 9 (2 (e^{x} + e^{x} x) + e^{x} x^{2} + 2 x e^{x})

Expand

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

= 9 (e^{x} x^{2} + 4 e^{x} x + 2 e^{x})

\int_{1}^{4} \frac{5}{x} d x

\int x^{2} (\frac{1}{x ^{3}} + \frac{1}{x}) d x

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

\int \frac{cos ( 4 x )}{1 + sin ^{2} ( 4 x )} d x

\int_{0}^{10} 1

What is the derivative of 9(2xe^x+e^xx^2) ?
The derivative of 9(2xe^x+e^xx^2) is 9(e^xx^2+4e^xx+2e^x)
What is the first derivative of 9(2xe^x+e^xx^2) ?
The first derivative of 9(2xe^x+e^xx^2) is 9(e^xx^2+4e^xx+2e^x)