derivative f(x)=(3x^3+9x+7)(x^2+8)

Lösung

ableitung von

f (x) = (3 x^{3} + 9 x + 7) (x^{2} + 8)

15 x^{4} + 99 x^{2} + 14 x + 72

Schritte zur Lösung

\frac{d}{d x} ((3 x^{3} + 9 x + 7) (x^{2} + 8))

Wende die Produktregel an:

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

f = 3 x^{3} + 9 x + 7, g = x^{2} + 8

= \frac{d}{d x} (3 x^{3} + 9 x + 7) (x^{2} + 8) + \frac{d}{d x} (x^{2} + 8) (3 x^{3} + 9 x + 7)

\frac{d}{d x} (3 x^{3} + 9 x + 7) = 9 x^{2} + 9

\frac{d}{d x} (x^{2} + 8) = 2 x

= (9 x^{2} + 9) (x^{2} + 8) + 2 x (3 x^{3} + 9 x + 7)

Vereinfache

(9 x^{2} + 9) (x^{2} + 8) + 2 x (3 x^{3} + 9 x + 7) : 15 x^{4} + 99 x^{2} + 14 x + 72

= 15 x^{4} + 99 x^{2} + 14 x + 72

so l v e f or x, f = f e^{\frac{1}{f}}

x \to - 2 - lim ([x])

d er i v a t i v e 2 + \frac{2}{x} + \frac{6}{x ^{2}}

\frac{\partial}{\partial y} (y^{x})

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