What is the derivative of e^{2x}(2x+1) ?

The derivative of e^{2x}(2x+1) is 4e^{2x}x+4e^{2x}

What is the first derivative of e^{2x}(2x+1) ?

The first derivative of e^{2x}(2x+1) is 4e^{2x}x+4e^{2x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

4 e^{2 x} x + 4 e^{2 x}

Solution steps

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

Apply the Product Rule:

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

f = e^{2 x}, g = 2 x + 1

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

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

\frac{d}{d x} (2 x + 1) = 2

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

Simplify

e^{2 x} \cdot 2 (2 x + 1) + 2 e^{2 x} : 4 e^{2 x} x + 4 e^{2 x}

= 4 e^{2 x} x + 4 e^{2 x}

What is the derivative of e^{2x}(2x+1) ?
The derivative of e^{2x}(2x+1) is 4e^{2x}x+4e^{2x}
What is the first derivative of e^{2x}(2x+1) ?
The first derivative of e^{2x}(2x+1) is 4e^{2x}x+4e^{2x}