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^6}

Solution

\frac{d}{d x} (x e^{x^{6}})

Solution

e^{x^{6}} + 6 e^{x^{6}} x^{6}

Solution steps

\frac{d}{d x} (x e^{x^{6}})

Apply the Product Rule:

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

f = x, g = e^{x^{6}}

= \frac{d x}{d x} e^{x^{6}} + \frac{d}{d x} (e^{x^{6}}) x

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

\frac{d}{d x} (e^{x^{6}}) = e^{x^{6}} \cdot 6 x^{5}

= 1 \cdot e^{x^{6}} + e^{x^{6}} \cdot 6 x^{5} x

Simplify

1 \cdot e^{x^{6}} + e^{x^{6}} \cdot 6 x^{5} x : e^{x^{6}} + 6 e^{x^{6}} x^{6}

= e^{x^{6}} + 6 e^{x^{6}} x^{6}

Graph

Popular Examples

derivative of 2(12)(18)+2(9)derivative of

2 (12) (18) + 2 (9)

(dr)/(dθ)=8cos(θ)

\frac{d r}{d θ} = 8 cos (θ)

\int 92

limit as t approaches 0 of ((3^t-2^t))/t

t \to 0 lim (\frac{( 3 ^{t} - 2 ^{t} )}{t})

integral of ((3x-2))/(1-6x-9x^2)

\int \frac{( 3 x - 2 )}{1 - 6 x - 9 x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of xe^{x^6} ?
The derivative of xe^{x^6} is e^{x^6}+6e^{x^6}x^6
What is the first derivative of xe^{x^6} ?
The first derivative of xe^{x^6} is e^{x^6}+6e^{x^6}x^6