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

The derivative of e^{2x}sqrt(x+1) is (4e^{2x}x+5e^{2x})/(2sqrt(x+1))

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

The first derivative of e^{2x}sqrt(x+1) is (4e^{2x}x+5e^{2x})/(2sqrt(x+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{4 e ^{2 x} x + 5 e ^{2 x}}{2 x + 1}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= e^{2 x} \cdot 2 x + 1 + \frac{1}{2 x + 1} e^{2 x}

Simplify

e^{2 x} \cdot 2 x + 1 + \frac{1}{2 x + 1} e^{2 x} : \frac{4 e ^{2 x} x + 5 e ^{2 x}}{2 x + 1}

= \frac{4 e ^{2 x} x + 5 e ^{2 x}}{2 x + 1}

\int_{2}^{\infty} y e^{- 8 y} d y

\frac{d}{d x} (cos^{2} (x^{2} + y^{2}))

\int_{2}^{\infty} 8 x^{- 2} d x

\int 7 - \frac{1}{7 x ^{2}} d x

x \to 0 lim ((1 - e^{x})^{x})

What is the derivative of e^{2x}sqrt(x+1) ?
The derivative of e^{2x}sqrt(x+1) is (4e^{2x}x+5e^{2x})/(2sqrt(x+1))
What is the first derivative of e^{2x}sqrt(x+1) ?
The first derivative of e^{2x}sqrt(x+1) is (4e^{2x}x+5e^{2x})/(2sqrt(x+1))