What is the derivative of (z^{8/3})/8-(e^{-2z})/2 ?

The derivative of (z^{8/3})/8-(e^{-2z})/2 is (z^{5/3})/3+e^{-2z}

What is the first derivative of (z^{8/3})/8-(e^{-2z})/2 ?

The first derivative of (z^{8/3})/8-(e^{-2z})/2 is (z^{5/3})/3+e^{-2z}

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derivative of

\frac{z ^{\frac{8}{3}}}{8} - \frac{e ^{- 2 z}}{2}

\frac{z ^{\frac{5}{3}}}{3} + e^{- 2 z}

Solution steps

\frac{d}{d z} (\frac{z ^{\frac{8}{3}}}{8} - \frac{e ^{- 2 z}}{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d z} (\frac{z ^{\frac{8}{3}}}{8}) - \frac{d}{d z} (\frac{e ^{- 2 z}}{2})

\frac{d}{d z} (\frac{z ^{\frac{8}{3}}}{8}) = \frac{z ^{\frac{5}{3}}}{3}

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

= \frac{z ^{\frac{5}{3}}}{3} - (- e^{- 2 z})

Simplify

= \frac{z ^{\frac{5}{3}}}{3} + e^{- 2 z}

\frac{d}{d x} (\frac{3 x + 4}{2 x - 5})

y^{^{''}} - 3 y^{^{'}} = 0

x \to \infty lim (7 x + 4)

f (x) = 2 x^{2} + 5 x

\int (3 x^{5} - 5 x^{9}) d x

What is the derivative of (z^{8/3})/8-(e^{-2z})/2 ?
The derivative of (z^{8/3})/8-(e^{-2z})/2 is (z^{5/3})/3+e^{-2z}
What is the first derivative of (z^{8/3})/8-(e^{-2z})/2 ?
The first derivative of (z^{8/3})/8-(e^{-2z})/2 is (z^{5/3})/3+e^{-2z}