derivative (2x-4)^4(x^2+x+1)^5

Lösung

ableitung von

(2 x - 4)^{4} (x^{2} + x + 1)^{5}

8 (2 x - 4)^{3} (x^{2} + x + 1)^{5} + 5 (x^{2} + x + 1)^{4} (2 x + 1) (2 x - 4)^{4}

Schritte zur Lösung

\frac{d}{d x} ((2 x - 4)^{4} (x^{2} + x + 1)^{5})

Wende die Produktregel an:

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

f = (2 x - 4)^{4}, g = (x^{2} + x + 1)^{5}

= \frac{d}{d x} ((2 x - 4)^{4}) (x^{2} + x + 1)^{5} + \frac{d}{d x} ((x^{2} + x + 1)^{5}) (2 x - 4)^{4}

\frac{d}{d x} ((2 x - 4)^{4}) = 8 (2 x - 4)^{3}

\frac{d}{d x} ((x^{2} + x + 1)^{5}) = 5 (x^{2} + x + 1)^{4} (2 x + 1)

= 8 (2 x - 4)^{3} (x^{2} + x + 1)^{5} + 5 (x^{2} + x + 1)^{4} (2 x + 1) (2 x - 4)^{4}

\int \frac{6 x ^{2}}{x ^{3} - 1} d x

in v erse l a pl a ce 3 s

d er i v a t i v e y = 7 x + 5

d er i v a t i v e 9 (x^{3} - x)^{4}

\frac{\partial}{\partial x} (5 sin (2 (5 x + 6 y)))