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Popular >

derivative of x^{4/3}+e^{-5x}

Solution

\frac{d}{d x} (x^{\frac{4}{3}} + e^{- 5 x})

Solution

\frac{4 x ^{\frac{1}{3}}}{3} - 5 e^{- 5 x}

Solution steps

\frac{d}{d x} (x^{\frac{4}{3}} + e^{- 5 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{\frac{4}{3}}) + \frac{d}{d x} (e^{- 5 x})

\frac{d}{d x} (x^{\frac{4}{3}}) = \frac{4 x ^{\frac{1}{3}}}{3}

\frac{d}{d x} (e^{- 5 x}) = - 5 e^{- 5 x}

= \frac{4 x ^{\frac{1}{3}}}{3} - 5 e^{- 5 x}

Graph

Popular Examples

y^{''}+18y^'+81y=0

y^{^{''}} + 18 y^{^{'}} + 81 y = 0

integral from 0 to (3pi)/2 of cos^3(25x)

\int_{0}^{\frac{3 π}{2}} cos^{3} (25 x) d x

5 x^{^{'}} - 4 x = 0

limit as x approaches 1 of ((\sqrt[6]{x}-1))/(x-1)

x \to 1 lim (\frac{( 6 x - 1 )}{x - 1})

y^{''}+10y^'+9y=9

y^{^{''}} + 10 y^{^{'}} + 9 y = 9

Frequently Asked Questions (FAQ)

What is the derivative of x^{4/3}+e^{-5x} ?
The derivative of x^{4/3}+e^{-5x} is (4x^{1/3})/3-5e^{-5x}
What is the first derivative of x^{4/3}+e^{-5x} ?
The first derivative of x^{4/3}+e^{-5x} is (4x^{1/3})/3-5e^{-5x}