en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=e^{-0.5x}(4-x)-2

Solution

derivative of

f (x) = e^{- 0.5 x} (4 - x) - 2

Solution

0.5 e^{- 0.5 x} x - 3 e^{- 0.5 x}

Solution steps

\frac{d}{d x} (e^{- 0.5 x} (4 - x) - 2)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{- 0.5 x} (4 - x)) - \frac{d}{d x} (2)

\frac{d}{d x} (e^{- 0.5 x} (4 - x)) = 0.5 e^{- 0.5 x} x - 3 e^{- 0.5 x}

\frac{d}{d x} (2) = 0

= 0.5 e^{- 0.5 x} x - 3 e^{- 0.5 x} - 0

Simplify

= 0.5 e^{- 0.5 x} x - 3 e^{- 0.5 x}

Popular Examples

sum from n=1 to infinity of 5/(4n^2-1)

n = 1 \sum \infty \frac{5}{4 n ^{2} - 1}

derivative of-3sin(6x)

\frac{d}{d x} (- 3 sin (6 x))

area 3x,(6x)/7 ,55-x^2 area

3 x, \frac{6 x}{7}, 55 - x^{2}

(\partial)/(\partial t)(e^{-t}cos(t))

\frac{\partial}{\partial t} (e^{- t} cos (t))

integral of 1/(x^3+xy^2)

\int \frac{1}{x ^{3} + x y ^{2}} d y

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=e^{-0.5x}(4-x)-2 ?
The derivative of f(x)=e^{-0.5x}(4-x)-2 is 0.5e^{-0.5x}x-3e^{-0.5x}
What is the first derivative of f(x)=e^{-0.5x}(4-x)-2 ?
The first derivative of f(x)=e^{-0.5x}(4-x)-2 is 0.5e^{-0.5x}x-3e^{-0.5x}