derivative f(z)=(9z^4+3z^2+1)(3z^3-z)

Lösung

ableitung von

f (z) = (9 z^{4} + 3 z^{2} + 1) (3 z^{3} - z)

189 z^{6} - 1

Schritte zur Lösung

\frac{d}{d z} ((9 z^{4} + 3 z^{2} + 1) (3 z^{3} - z))

Wende die Produktregel an:

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

f = 9 z^{4} + 3 z^{2} + 1, g = 3 z^{3} - z

= \frac{d}{d z} (9 z^{4} + 3 z^{2} + 1) (3 z^{3} - z) + \frac{d}{d z} (3 z^{3} - z) (9 z^{4} + 3 z^{2} + 1)

\frac{d}{d z} (9 z^{4} + 3 z^{2} + 1) = 36 z^{3} + 6 z

\frac{d}{d z} (3 z^{3} - z) = 9 z^{2} - 1

= (36 z^{3} + 6 z) (3 z^{3} - z) + (9 z^{2} - 1) (9 z^{4} + 3 z^{2} + 1)

Vereinfache

(36 z^{3} + 6 z) (3 z^{3} - z) + (9 z^{2} - 1) (9 z^{4} + 3 z^{2} + 1) : 189 z^{6} - 1

= 189 z^{6} - 1

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

x \to - 8 lim (9 x + 10)

\frac{( d x )}{( d y )} = \frac{8 - ( 2 x )}{( 100 + 2 y )}

d er i v a t i v e f (x) = e^{x 7 x + 6}

in v erse l a pl a ce \frac{7}{2 s ^{2 + 8}}