d/(dy)((x(y))(1+7y)^8)

Lösung

\frac{d}{d y} ((x (y)) (1 + 7 y)^{8})

x ((1 + 7 y)^{8} + 56 y (1 + 7 y)^{7})

Schritte zur Lösung

\frac{d}{d y} ((x (y)) (1 + 7 y)^{8})

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{d}{d y} (y (1 + 7 y)^{8})

Wende die Produktregel an:

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

f = y, g = (1 + 7 y)^{8}

= x (\frac{d y}{d y} (1 + 7 y)^{8} + \frac{d}{d y} ((1 + 7 y)^{8}) y)

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

\frac{d}{d y} ((1 + 7 y)^{8}) = 56 (1 + 7 y)^{7}

= x (1 \cdot (1 + 7 y)^{8} + 56 (1 + 7 y)^{7} y)

Vereinfache

= x ((1 + 7 y)^{8} + 56 y (1 + 7 y)^{7})

e x p an d tan (θ) (cot (θ) - cos (θ))

\frac{d ^{2}}{d k ^{2}} ((y (k, x)) (e^{2 x} - k x))

s im pl i f y (1 + 4 y i)^{2}

e x p an d (cot (x) - 3) (csc (x) + 2)

e x p an d (3 x y^{2} - 4 y) + (3 x - 4 x^{2} y) \frac{d y}{d x}