What is the derivative of 4x^3e^x+e^xx^4 ?

The derivative of 4x^3e^x+e^xx^4 is e^xx^4+8e^xx^3+12e^xx^2

What is the first derivative of 4x^3e^x+e^xx^4 ?

The first derivative of 4x^3e^x+e^xx^4 is e^xx^4+8e^xx^3+12e^xx^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

4 x^{3} e^{x} + e^{x} x^{4}

e^{x} x^{4} + 8 e^{x} x^{3} + 12 e^{x} x^{2}

Solution steps

\frac{d}{d x} (4 x^{3} e^{x} + e^{x} x^{4})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 x^{3} e^{x}) + \frac{d}{d x} (e^{x} x^{4})

\frac{d}{d x} (4 x^{3} e^{x}) = 4 (3 x^{2} e^{x} + e^{x} x^{3})

\frac{d}{d x} (e^{x} x^{4}) = e^{x} x^{4} + 4 x^{3} e^{x}

= 4 (3 x^{2} e^{x} + e^{x} x^{3}) + e^{x} x^{4} + 4 x^{3} e^{x}

Simplify

4 (3 x^{2} e^{x} + e^{x} x^{3}) + e^{x} x^{4} + 4 x^{3} e^{x} : e^{x} x^{4} + 8 e^{x} x^{3} + 12 e^{x} x^{2}

= e^{x} x^{4} + 8 e^{x} x^{3} + 12 e^{x} x^{2}

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

\int 2^{x} 3^{2 x} 5^{3 x} d x

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

x \to - 7 - lim (\frac{x + 3}{x + 7})

\int \frac{t ^{2} + 1}{t} d t

What is the derivative of 4x^3e^x+e^xx^4 ?
The derivative of 4x^3e^x+e^xx^4 is e^xx^4+8e^xx^3+12e^xx^2
What is the first derivative of 4x^3e^x+e^xx^4 ?
The first derivative of 4x^3e^x+e^xx^4 is e^xx^4+8e^xx^3+12e^xx^2