derivative f(x)=(x^2+1)(x^3+1)

Lösung

ableitung von

f (x) = (x^{2} + 1) (x^{3} + 1)

5 x^{4} + 3 x^{2} + 2 x

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + 1) (x^{3} + 1))

Wende die Produktregel an:

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

f = x^{2} + 1, g = x^{3} + 1

= \frac{d}{d x} (x^{2} + 1) (x^{3} + 1) + \frac{d}{d x} (x^{3} + 1) (x^{2} + 1)

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

\frac{d}{d x} (x^{3} + 1) = 3 x^{2}

= 2 x (x^{3} + 1) + 3 x^{2} (x^{2} + 1)

Vereinfache

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

= 5 x^{4} + 3 x^{2} + 2 x

\frac{\partial}{\partial z} (x + e^{z} + y)

x y^{^{'}} + ln (x) y = 0

d er i v a t i v e f (x) = 2 x^{3} + 3 x^{2} - 12 x + 2

x \to 4 - lim (\frac{x + 5}{x - 4})

t an g e n t y = x^{2} + 2 x - 1, (1, 2)