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

Lösung

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

\frac{e ^{x} ( - 4 - 3 x ^{\frac{13}{6}} )}{3 x ^{\frac{3}{2}}} + e^{x} (- \frac{2}{3 x ^{\frac{1}{3}}} + \frac{2}{x ^{\frac{5}{2}}})

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = - x^{\frac{2}{3}} - \frac{4}{3} x^{- \frac{3}{2}}

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

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

\frac{d}{d x} (- x^{\frac{2}{3}} - \frac{4}{3} x^{- \frac{3}{2}}) = - \frac{2}{3 x ^{\frac{1}{3}}} + \frac{2}{x ^{\frac{5}{2}}}

= e^{x} (- x^{\frac{2}{3}} - \frac{4}{3} x^{- \frac{3}{2}}) + (- \frac{2}{3 x ^{\frac{1}{3}}} + \frac{2}{x ^{\frac{5}{2}}}) e^{x}

e^{x} (- x^{\frac{2}{3}} - \frac{4}{3} x^{- \frac{3}{2}}) = \frac{e ^{x} ( - 4 - 3 x ^{\frac{13}{6}} )}{3 x ^{\frac{3}{2}}}

= \frac{e ^{x} ( - 4 - 3 x ^{\frac{13}{6}} )}{3 x ^{\frac{3}{2}}} + e^{x} (- \frac{2}{3 x ^{\frac{1}{3}}} + \frac{2}{x ^{\frac{5}{2}}})

\int x^{2} (x^{3} + 2)^{4} d x

\int_{0}^{1} x (1 - x)^{2} d x

x \to + (- 2) lim (x^{2} - x + 4)

y^{^{''}} - 6 y^{^{'}} + 9 y = 4 t e^{3 t}

d er i v a t i v e f (x) = ln (9 sin^{2} (x))