derivative of (x+1(x+1-1/(x+2)))

Lösung

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

\frac{2 x ^{3} + 8 x ^{2} + 8 x - 1}{( x + 2 ) ^{2}} + 2

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x + 1, g = x + 1 - \frac{1}{x + 2}

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

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

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

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

Vereinfache

1 \cdot (x + 1 - \frac{1}{x + 2}) + (\frac{1}{( x + 2 ) ^{2}} + 1) (x + 1) : \frac{2 x ^{3} + 8 x ^{2} + 8 x - 1}{( x + 2 ) ^{2}} + 2

= \frac{2 x ^{3} + 8 x ^{2} + 8 x - 1}{( x + 2 ) ^{2}} + 2

\int_{0}^{π} 3 sin^{4} (3 t) d t

in v erse l a pl a ce \frac{15}{( s + 10 ) ( s + 11 )}

\int_{0}^{2.8} 0.2 x d x

d er i v a t i v e \frac{4 π r ^{3}}{3}

p a r t ia l f r a c t i o n \frac{x ^{3}}{x + 1}