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}}

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}