derivative of ((x^2+2x/(x+1))^5)

Lösung

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

\frac{5 ( x ^{2} + 2 x ) ^{4} ( x ^{2} + 2 x + 2 )}{( x + 1 ) ^{6}}

Schritte zur Lösung

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

Wende die Kettenregel an:

5 (\frac{x ^{2} + 2 x}{x + 1})^{4} \frac{d}{d x} (\frac{x ^{2} + 2 x}{x + 1})

= 5 (\frac{x ^{2} + 2 x}{x + 1})^{4} \frac{d}{d x} (\frac{x ^{2} + 2 x}{x + 1})

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

= 5 (\frac{x ^{2} + 2 x}{x + 1})^{4} \frac{x ^{2} + 2 x + 2}{( x + 1 ) ^{2}}

Vereinfache

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

= \frac{5 ( x ^{2} + 2 x ) ^{4} ( x ^{2} + 2 x + 2 )}{( x + 1 ) ^{6}}

2 y^{^{'}} = 3 x y + 1

x \to 1 lim ((x^{2} - 2 x + 1) cos (e^{\frac{1}{x - 1}}))

x \to \infty lim ([2, x])

\int (sin^{2} (x) - cos^{2} (x)) d x

\frac{d ^{5}}{d x ^{5}} (\frac{1}{x})