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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

\frac{d}{d t} (100 - 10 t + 6 t^{2})

y = x^{7} + 3 x^{5} + 1

4 x^{\frac{1}{3}}

2 sin^{2} (t) + 8 cos^{2} (t)

\frac{( x + 2 ) ^{2}}{3}

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