en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of xe^{x^4}

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{x^{4}}

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{x^{4}} + e^{x^{4}} \cdot 4 x^{3} x

Simplify

1 \cdot e^{x^{4}} + e^{x^{4}} \cdot 4 x^{3} x : e^{x^{4}} + 4 e^{x^{4}} x^{4}

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

Popular Examples

d/(d{z)}({x}^2{y}{z})

\frac{d}{d z} (x^{2} y z)

integral of x^5*ln(x)

\int x^{5} \cdot ln (x) d x

y^{^{''}} + 9 y = 19

derivative of f(x)=(x^2)/(8-8x)derivative of

f (x) = \frac{x ^{2}}{8 - 8 x}

derivative of (1/(y^2)-5/(y^4))(y+9y^3)derivative of

(\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 9 y^{3})

Frequently Asked Questions (FAQ)

What is the derivative of xe^{x^4} ?
The derivative of xe^{x^4} is e^{x^4}+4e^{x^4}x^4
What is the first derivative of xe^{x^4} ?
The first derivative of xe^{x^4} is e^{x^4}+4e^{x^4}x^4