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Popular >

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

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

derivative of (x^4)/(2-x^3)derivative of

\frac{x ^{4}}{2 - x ^{3}}

derivative of 47x^3-75sqrt(x)

\frac{d}{d x} (47 x^{3} - 75 x)

y^{''}+7y^'+10y=10te^{4t}

y^{^{''}} + 7 y^{^{'}} + 10 y = 10 t e^{4 t}

integral from 0 to 1 of (57)/(x^5)

\int_{0}^{1} \frac{57}{x ^{5}} d x

integral of (2x)/((x^3-1))

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

Frequently Asked Questions (FAQ)

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