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

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

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

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

Popular >

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

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

Solution steps

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

Simplify

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

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

x \to + 3 lim (\frac{8}{x - 3})

5 x, \frac{5}{x}, 0, 5

\int_{0}^{\frac{π}{4}} 6 tan^{3} (x) d x

\frac{\partial}{\partial y} ((2 x - y + 5)^{2})

f (x) = (4 x^{2} - 5 x) e^{x}

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