derivative (2+u^2)^5(5-9u^2)^8

Lösung

ableitung von

(2 + u^{2})^{5} (5 - 9 u^{2})^{8}

10 u (2 + u^{2})^{4} (5 - 9 u^{2})^{8} - 144 u (5 - 9 u^{2})^{7} (2 + u^{2})^{5}

Schritte zur Lösung

\frac{d}{d u} ((2 + u^{2})^{5} (5 - 9 u^{2})^{8})

Wende die Produktregel an:

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

f = (2 + u^{2})^{5}, g = (5 - 9 u^{2})^{8}

= \frac{d}{d u} ((2 + u^{2})^{5}) (5 - 9 u^{2})^{8} + \frac{d}{d u} ((5 - 9 u^{2})^{8}) (2 + u^{2})^{5}

\frac{d}{d u} ((2 + u^{2})^{5}) = 10 u (2 + u^{2})^{4}

\frac{d}{d u} ((5 - 9 u^{2})^{8}) = - 144 u (5 - 9 u^{2})^{7}

= 10 u (2 + u^{2})^{4} (5 - 9 u^{2})^{8} + (- 144 u (5 - 9 u^{2})^{7}) (2 + u^{2})^{5}

Vereinfache

= 10 u (2 + u^{2})^{4} (5 - 9 u^{2})^{8} - 144 u (5 - 9 u^{2})^{7} (2 + u^{2})^{5}

t an g e n t f (x) = 5 + 4 x^{2} - 2 x^{3}, (1, 7)

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

\frac{d}{d x} (\frac{sin ( x )}{1 + cos ( x )})

\int e^{- s t} t cos (t) d t

in v erse l a pl a ce \frac{5}{s ( s ^{2} + s + 1 )}