What is the derivative of-4/5 e^{(2/3 x}) ?

The derivative of-4/5 e^{(2/3 x}) is -8/15 e^{(2x)/3}

What is the first derivative of-4/5 e^{(2/3 x}) ?

The first derivative of-4/5 e^{(2/3 x}) is -8/15 e^{(2x)/3}

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

- \frac{8}{15} e^{\frac{2 x}{3}}

Solution steps

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

Simplify

- \frac{4}{5} e^{(\frac{2}{3} x)} : - \frac{4}{5} e^{\frac{2 x}{3}}

= \frac{d}{d x} (- \frac{4}{5} e^{\frac{2 x}{3}})

Take the constant out:

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

= - \frac{4}{5} \frac{d}{d x} (e^{\frac{2 x}{3}})

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{2 x}{3}) = \frac{2}{3}

= - \frac{4}{5} e^{\frac{2 x}{3}} \frac{2}{3}

Simplify

- \frac{4}{5} e^{\frac{2 x}{3}} \frac{2}{3} : - \frac{8}{15} e^{\frac{2 x}{3}}

= - \frac{8}{15} e^{\frac{2 x}{3}}

\frac{d}{d x} ((1 + x^{2} sin (x))^{4})

\int \frac{2 x + 7}{( 2 x ^{2} + 14 x ) ^{4}} d x

\int sin (x) (1 + cos (x))^{4} d x

\frac{\partial}{\partial y} (x^{2} + y^{2} - z^{2})

e^{- t} (\frac{e ^{t} + e ^{- t}}{2})

What is the derivative of-4/5 e^{(2/3 x}) ?
The derivative of-4/5 e^{(2/3 x}) is -8/15 e^{(2x)/3}
What is the first derivative of-4/5 e^{(2/3 x}) ?
The first derivative of-4/5 e^{(2/3 x}) is -8/15 e^{(2x)/3}