d/(dy)((x)((1+6x)^4))

Lösung

\frac{d}{d y} ((y) ((1 + 6 y)^{4}))

(1 + 6 y)^{4} + 24 y (1 + 6 y)^{3}

Schritte zur Lösung

\frac{d}{d y} ((y) ((1 + 6 y)^{4}))

Wende die Produktregel an:

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

f = y, g = (1 + 6 y)^{4}

= \frac{d y}{d y} (1 + 6 y)^{4} + \frac{d}{d y} ((1 + 6 y)^{4}) y

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

\frac{d}{d y} ((1 + 6 y)^{4}) = 24 (1 + 6 y)^{3}

= 1 \cdot (1 + 6 y)^{4} + 24 (1 + 6 y)^{3} y

Vereinfache

= (1 + 6 y)^{4} + 24 y (1 + 6 y)^{3}

e x p an d (x - 8) \cdot (x + 64)

e x p an d \frac{1}{1 - x} - \frac{1}{x}

e x p an d \frac{1}{3} (cosh (9 e ni) - cosh (6 e ni))

e x p an d (77 + 4 x - x^{2}) d x

s im pl i f y (s + 2 + j^{2} 3) (s + 2 - j^{2} 3) (s + 10)