d/(dy)((x)((1+2x)^6))

Lösung

\frac{d}{d y} ((y) ((1 + 2 y)^{6}))

(1 + 2 y)^{6} + 12 y (1 + 2 y)^{5}

Schritte zur Lösung

\frac{d}{d y} ((y) ((1 + 2 y)^{6}))

Wende die Produktregel an:

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

f = y, g = (1 + 2 y)^{6}

= \frac{d y}{d y} (1 + 2 y)^{6} + \frac{d}{d y} ((1 + 2 y)^{6}) y

\frac{d y}{d y} = 1

\frac{d}{d y} ((1 + 2 y)^{6}) = 12 (1 + 2 y)^{5}

= 1 \cdot (1 + 2 y)^{6} + 12 (1 + 2 y)^{5} y

Vereinfache

= (1 + 2 y)^{6} + 12 y (1 + 2 y)^{5}

s im pl i f y 3 (1 - 2 sin^{2} (x) cos^{2} (x))

e x p an d a (- 3, - 2) b (5, 3)

s im pl i f y (x + 15 + x)^{2}

s im pl i f y 2 (2 x cos^{3} (x) - 3 x^{2} cos^{2} (x) sin (x))

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