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

解答

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

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

求解步骤

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

化简

- \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}})

将常数提出:

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

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

使用连锁律:

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}

化简

- \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}}

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