derivative of (x^5+2x(x^3+x^2+x+7))

Lösung

\frac{d}{d x} ((x^{5} + 2 x) (x^{3} + x^{2} + x + 7))

8 x^{7} + 7 x^{6} + 6 x^{5} + 35 x^{4} + 8 x^{3} + 6 x^{2} + 4 x + 14

Schritte zur Lösung

\frac{d}{d x} ((x^{5} + 2 x) (x^{3} + x^{2} + x + 7))

Wende die Produktregel an:

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

f = x^{5} + 2 x, g = x^{3} + x^{2} + x + 7

= \frac{d}{d x} (x^{5} + 2 x) (x^{3} + x^{2} + x + 7) + \frac{d}{d x} (x^{3} + x^{2} + x + 7) (x^{5} + 2 x)

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

\frac{d}{d x} (x^{3} + x^{2} + x + 7) = 3 x^{2} + 2 x + 1

= (5 x^{4} + 2) (x^{3} + x^{2} + x + 7) + (3 x^{2} + 2 x + 1) (x^{5} + 2 x)

Vereinfache

(5 x^{4} + 2) (x^{3} + x^{2} + x + 7) + (3 x^{2} + 2 x + 1) (x^{5} + 2 x) : 8 x^{7} + 7 x^{6} + 6 x^{5} + 35 x^{4} + 8 x^{3} + 6 x^{2} + 4 x + 14

= 8 x^{7} + 7 x^{6} + 6 x^{5} + 35 x^{4} + 8 x^{3} + 6 x^{2} + 4 x + 14

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

a re a y = 9 x^{2} ln (x), y = 36 ln (x)

l a pl a ce t r an s f or m cos^{2} (t)

x \to - 1 lim (x^{3} + x^{2} - 6 x + 9)

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