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

The derivative of e^{x/2} 1/2 is 1/4 e^{x/2}

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

The first derivative of e^{x/2} 1/2 is 1/4 e^{x/2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2} e^{\frac{x}{2}} \frac{1}{2} : \frac{1}{4} e^{\frac{x}{2}}

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

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