derivative of 2x^{5/3}-5x^{4/5}+7x^{3/2}-8x+17

Lösung

\frac{d}{d x} (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{5}} + 7 x^{\frac{3}{2}} - 8 x + 17)

\frac{20 x ^{\frac{13}{15}} + 63 x ^{\frac{7}{10}} - 24}{6 x ^{\frac{1}{5}}} - 8

Schritte zur Lösung

\frac{d}{d x} (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{5}} + 7 x^{\frac{3}{2}} - 8 x + 17)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x^{\frac{5}{3}}) - \frac{d}{d x} (5 x^{\frac{4}{5}}) + \frac{d}{d x} (7 x^{\frac{3}{2}}) - \frac{d}{d x} (8 x) + \frac{d}{d x} (17)

\frac{d}{d x} (2 x^{\frac{5}{3}}) = \frac{10 x ^{\frac{2}{3}}}{3}

\frac{d}{d x} (5 x^{\frac{4}{5}}) = \frac{4}{x ^{\frac{1}{5}}}

\frac{d}{d x} (7 x^{\frac{3}{2}}) = \frac{21 x ^{\frac{1}{2}}}{2}

\frac{d}{d x} (8 x) = 8

\frac{d}{d x} (17) = 0

= \frac{10 x ^{\frac{2}{3}}}{3} - \frac{4}{x ^{\frac{1}{5}}} + \frac{21 x ^{\frac{1}{2}}}{2} - 8 + 0

Vereinfache

\frac{10 x ^{\frac{2}{3}}}{3} - \frac{4}{x ^{\frac{1}{5}}} + \frac{21 x ^{\frac{1}{2}}}{2} - 8 + 0 : \frac{20 x ^{\frac{13}{15}} + 63 x ^{\frac{7}{10}} - 24}{6 x ^{\frac{1}{5}}} - 8

= \frac{20 x ^{\frac{13}{15}} + 63 x ^{\frac{7}{10}} - 24}{6 x ^{\frac{1}{5}}} - 8

\int arcsin^{2} (x) d x

d er i v a t i v e f (x) = \frac{x ^{2}}{x - 11}

d er i v a t i v e 5 x^{3} + 2 x^{2} + 3

x \to \infty lim (co x (x))

\frac{\partial}{\partial s} (- 5 s^{2} t)