en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^{2x}n(3x)

Solution

\frac{d}{d x} (e^{2 x} n (3 x))

Solution

3 n (2 e^{2 x} x + e^{2 x})

Solution steps

\frac{d}{d x} (e^{2 x} n (3 x))

Take the constant out:

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

= n \cdot 3 \frac{d}{d x} (e^{2 x} x)

Apply the Product Rule:

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

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

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

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

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

= n \cdot 3 (e^{2 x} \cdot 2 x + 1 \cdot e^{2 x})

Simplify

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

Popular Examples

derivative of 3/8 pir^3 derivative of

\frac{3}{8} π r^{3}

limit as x approaches 0 of 8csc(x)-8/x

x \to 0 lim (8 csc (x) - \frac{8}{x})

sum from n=0 to infinity of 1^{-n}

n = 0 \sum \infty 1^{- n}

integral of (3sqrt(x))

\int (3 x) d x

integral from 0 to 1 of arcsin(y)

\int_{0}^{1} arcsin (y) d y

Frequently Asked Questions (FAQ)

What is the derivative of e^{2x}n(3x) ?
The derivative of e^{2x}n(3x) is 3n(2e^{2x}x+e^{2x})
What is the first derivative of e^{2x}n(3x) ?
The first derivative of e^{2x}n(3x) is 3n(2e^{2x}x+e^{2x})