derivative of-4/5 e^{(2/3 x})

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

- \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}})

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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}

Vereinfache

- \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}}

\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})

l a pl a ce t r an s f or m e^{- t} (\frac{e ^{t} + e ^{- t}}{2})

t an g e n t f (x) = \frac{25 x ^{3}}{3} + 10 x^{2} + 4 x - 7