derivative of-4x^{4/3}-2x^{-3/4}+3

Lösung

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

\frac{- 32 x ^{\frac{25}{12}} + 9}{6 x ^{\frac{7}{4}}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (4 x^{\frac{4}{3}}) = \frac{16 x ^{\frac{1}{3}}}{3}

\frac{d}{d x} (2 x^{- \frac{3}{4}}) = - \frac{3}{2 x ^{\frac{7}{4}}}

\frac{d}{d x} (3) = 0

= - \frac{16 x ^{\frac{1}{3}}}{3} - (- \frac{3}{2 x ^{\frac{7}{4}}}) + 0

Vereinfache

- \frac{16 x ^{\frac{1}{3}}}{3} - (- \frac{3}{2 x ^{\frac{7}{4}}}) + 0 : \frac{- 32 x ^{\frac{25}{12}} + 9}{6 x ^{\frac{7}{4}}}

= \frac{- 32 x ^{\frac{25}{12}} + 9}{6 x ^{\frac{7}{4}}}

d er i v a t i v e y = sec (x)

\int - e^{1 - x} d x

\int \frac{2 y}{x} d x

\frac{\partial}{\partial r} (\frac{1}{3} π r^{2} h)

d er i v a t i v e f (x) = \frac{( 5 x - 2 )}{( x ^{2} + 1 )}