derivative of (1+2x+3x^2+4x^3^{100})

Lösung

\frac{d}{d x} ((1 + 2 x + 3 x^{2} + 4 x^{3})^{100})

100 (1 + 2 x + 3 x^{2} + 4 x^{3})^{99} (12 x^{2} + 6 x + 2)

Schritte zur Lösung

\frac{d}{d x} ((1 + 2 x + 3 x^{2} + 4 x^{3})^{100})

Wende die Kettenregel an:

100 (1 + 2 x + 3 x^{2} + 4 x^{3})^{99} \frac{d}{d x} (1 + 2 x + 3 x^{2} + 4 x^{3})

= 100 (1 + 2 x + 3 x^{2} + 4 x^{3})^{99} \frac{d}{d x} (1 + 2 x + 3 x^{2} + 4 x^{3})

\frac{d}{d x} (1 + 2 x + 3 x^{2} + 4 x^{3}) = 12 x^{2} + 6 x + 2

= 100 (1 + 2 x + 3 x^{2} + 4 x^{3})^{99} (12 x^{2} + 6 x + 2)

in v erse l a pl a ce \frac{10}{( s - 2 ) ( s ^{3} + s )}

2 t y^{^{'}} = 4 y

\frac{d P}{d t} = 0.08 P (1 - \frac{P}{1000})

\int \frac{x ^{2}}{( 21 + 4 x - x ^{2} )} d x

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