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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

a re a f (x) = 4 - x, - 2, 6

\int_{5}^{9} \frac{2}{x ^{3}} d x

\int e^{3 x} 1 + 2 e^{3 x} d x

\frac{\partial}{\partial x} (1 - 2 x^{2} - 2 y)

(1 - t^{2}) y^{^{''}} - 2 t y^{^{'}} + 2 y = 0