en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 0.5e^{-0.5(x-1})

Solution

\frac{d}{d x} (0.5 e^{- 0.5 (x - 1)})

Solution

- 0.25 e^{- 0.5 (x - 1)}

Solution steps

\frac{d}{d x} (0.5 e^{- 0.5 (x - 1)})

Take the constant out:

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

= 0.5 \frac{d}{d x} (e^{- 0.5 (x - 1)})

Apply the chain rule:

e^{- 0.5 (x - 1)} \frac{d}{d x} (- 0.5 (x - 1))

= e^{- 0.5 (x - 1)} \frac{d}{d x} (- 0.5 (x - 1))

\frac{d}{d x} (- 0.5 (x - 1)) = - 0.5

= 0.5 e^{- 0.5 (x - 1)} (- 0.5)

Simplify

= - 0.25 e^{- 0.5 (x - 1)}

Popular Examples

81y^{''}+144y^'+64y=0

81 y^{^{''}} + 144 y^{^{'}} + 64 y = 0

(\partial)/(\partial x)(1/(2cos^2(x)))

\frac{\partial}{\partial x} (\frac{1}{2 cos ^{2} ( x )})

limit as x approaches infinity of arcsec(x)

x \to \infty lim (arcsec (x))

integral of 3x^2+x

\int 3 x^{2} + x d x

limit as x approaches 10-of 1/((x-10)^2)

x \to 10 - lim (\frac{1}{( x - 10 ) ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of 0.5e^{-0.5(x-1}) ?
The derivative of 0.5e^{-0.5(x-1}) is -0.25e^{-0.5(x-1)}
What is the first derivative of 0.5e^{-0.5(x-1}) ?
The first derivative of 0.5e^{-0.5(x-1}) is -0.25e^{-0.5(x-1)}