derivative of (x^2+2(x^3+1))

Lösung

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

5 x^{4} + 6 x^{2} + 2 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 x (x^{3} + 1) + 3 x^{2} (x^{2} + 2) : 5 x^{4} + 6 x^{2} + 2 x

= 5 x^{4} + 6 x^{2} + 2 x

\frac{d}{d x} (ln (x + y - 1))

x^{2} (\frac{d y}{d x}) = y - y x

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

\int (3 x^{2} + ln (x)) d x

\int_{- 5}^{5} \frac{y}{25 - y ^{2}} d y