derivative of 4x^{-1/3}+9/(x^{5/3})

Lösung

\frac{d}{d x} (4 x^{- \frac{1}{3}} + \frac{9}{x ^{\frac{5}{3}}})

- \frac{4}{3 x ^{\frac{4}{3}}} - \frac{15}{x ^{\frac{8}{3}}}

Schritte zur Lösung

\frac{d}{d x} (4 x^{- \frac{1}{3}} + \frac{9}{x ^{\frac{5}{3}}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (4 x^{- \frac{1}{3}}) + \frac{d}{d x} (\frac{9}{x ^{\frac{5}{3}}})

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

\frac{d}{d x} (\frac{9}{x ^{\frac{5}{3}}}) = - \frac{15}{x ^{\frac{8}{3}}}

= - \frac{4}{3 x ^{\frac{4}{3}}} - \frac{15}{x ^{\frac{8}{3}}}

im pl i c i t \frac{d y}{d x}, x cos (2 x + 3 y) = y sin (x)

\int 2 t - t - \frac{9}{t ^{2}} d t

x \to 0 lim (x^{2} - 4)

\int \frac{x ^{2}}{( 1 - y ^{2} )}

roo t s e^{a x}