en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 2e^{-2x}+1/3 e^x

Solution

\frac{d}{d x} (2 e^{- 2 x} + \frac{1}{3} e^{x})

Solution

- 4 e^{- 2 x} + \frac{1}{3} e^{x}

Solution steps

\frac{d}{d x} (2 e^{- 2 x} + \frac{1}{3} e^{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 e^{- 2 x}) + \frac{d}{d x} (\frac{1}{3} e^{x})

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

\frac{d}{d x} (\frac{1}{3} e^{x}) = \frac{1}{3} e^{x}

= - 4 e^{- 2 x} + \frac{1}{3} e^{x}

Popular Examples

derivative of 6^{x^2-3}

\frac{d}{d x} (6^{x^{2} - 3})

integral from 0 to pi/2 of sin^3(x/2)

\int_{0}^{\frac{π}{2}} sin^{3} (\frac{x}{2}) d x

derivative of (x-sqrt(x)/(x^2))

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

integral of (x^2)/(x^2-6x+9)

\int \frac{x ^{2}}{x ^{2} - 6 x + 9} d x

tangent of y=(|x|)/(sqrt(5-x^2)),(2,2)tangent of

y = \frac{∣ x ∣}{5 - x ^{2}}, (2, 2)

Frequently Asked Questions (FAQ)

What is the derivative of 2e^{-2x}+1/3 e^x ?
The derivative of 2e^{-2x}+1/3 e^x is -4e^{-2x}+1/3 e^x
What is the first derivative of 2e^{-2x}+1/3 e^x ?
The first derivative of 2e^{-2x}+1/3 e^x is -4e^{-2x}+1/3 e^x