erweitern d/(d^4)(y=2x^4-6x^3+7x^2+5x)

Lösung

erweitern

\frac{d}{d ^{4}} (y = 2 x^{4} - 6 x^{3} + 7 x^{2} + 5 x)

\frac{y}{d ^{3}} = 2 x^{4} - \frac{6 x ^{3}}{d ^{3}} + \frac{7 x ^{2}}{d ^{3}} + \frac{5 x}{d ^{3}}

Schritte zur Lösung

\frac{d}{d ^{4}} (y = 2 x^{4} - 6 x^{3} + 7 x^{2} + 5 x)

= \frac{d}{d ^{4}} (2 = x^{4} y - 6 x^{3} + 7 x^{2} + 5 x)

Setze Klammern

\frac{d}{d ^{4}} y = 2 x^{4} + \frac{d}{d ^{4}} (- 6 x^{3}) + \frac{d}{d ^{4}} \cdot 7 x^{2} + \frac{d}{d ^{4}} \cdot 5 x

Wende Minus-Plus Regeln an

+ (- a) = - a

\frac{d}{d ^{4}} y = 2 x^{4} - 6 \cdot \frac{d}{d ^{4}} x^{3} + 7 \cdot \frac{d}{d ^{4}} x^{2} + 5 \cdot \frac{d}{d ^{4}} x

Vereinfache

\frac{d}{d ^{4}} y = 2 x^{4} - 6 \cdot \frac{d}{d ^{4}} x^{3} + 7 \cdot \frac{d}{d ^{4}} x^{2} + 5 \cdot \frac{d}{d ^{4}} x : \frac{y}{d ^{3}} = 2 x^{4} - \frac{6 x ^{3}}{d ^{3}} + \frac{7 x ^{2}}{d ^{3}} + \frac{5 x}{d ^{3}}

\frac{y}{d ^{3}} = 2 x^{4} - \frac{6 x ^{3}}{d ^{3}} + \frac{7 x ^{2}}{d ^{3}} + \frac{5 x}{d ^{3}}

e x p an d (y - 2) + (x + 7) y^{'} (x)

e x p an d (1 - t) \cdot (0, 1, 0)

e x p an d 3 x^{2} e^{3 x} (1 + x)

e x p an d \frac{2 ( - x + 8 )}{5 e ^{\frac{x}{10}} x ^{\frac{1}{5}}}

s im pl i f y (r - 5)^{2}