derivative f(0)=(x^4+3x)(4x^5+4x-2)

Lösung

ableitung von

f (0) = (x^{4} + 3 x) (4 x^{5} + 4 x - 2)

36 x^{8} + 72 x^{5} + 20 x^{4} - 8 x^{3} + 24 x - 6

Schritte zur Lösung

\frac{d}{d x} ((x^{4} + 3 x) (4 x^{5} + 4 x - 2))

Wende die Produktregel an:

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

f = x^{4} + 3 x, g = 4 x^{5} + 4 x - 2

= \frac{d}{d x} (x^{4} + 3 x) (4 x^{5} + 4 x - 2) + \frac{d}{d x} (4 x^{5} + 4 x - 2) (x^{4} + 3 x)

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

\frac{d}{d x} (4 x^{5} + 4 x - 2) = 20 x^{4} + 4

= (4 x^{3} + 3) (4 x^{5} + 4 x - 2) + (20 x^{4} + 4) (x^{4} + 3 x)

Vereinfache

(4 x^{3} + 3) (4 x^{5} + 4 x - 2) + (20 x^{4} + 4) (x^{4} + 3 x) : 36 x^{8} + 72 x^{5} + 20 x^{4} - 8 x^{3} + 24 x - 6

= 36 x^{8} + 72 x^{5} + 20 x^{4} - 8 x^{3} + 24 x - 6

d er i v a t i v e - \frac{2}{x ^{2}}

d er i v a t i v e y = ln (\frac{x - 3}{x + 3})

\int (y^{5} - 5 y) d y

t a y l or e^{s i n (x)}

t an g e n t f (x) = x^{3} + 3 x - 2, at x = 3