d/(dy)((x(y))(y^2-1))

Lösung

\frac{d}{d y} ((x (y)) (y^{2} - 1))

x (3 y^{2} - 1)

Schritte zur Lösung

\frac{d}{d y} ((x (y)) (y^{2} - 1))

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{d}{d y} (y (y^{2} - 1))

Wende die Produktregel an:

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

f = y, g = y^{2} - 1

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

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

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

= x (1 \cdot (y^{2} - 1) + 2 yy)

Vereinfache

x (1 \cdot (y^{2} - 1) + 2 yy) : x (3 y^{2} - 1)

= x (3 y^{2} - 1)

e x p an d (3 i, - 1 j, - 1 k) \cdot (2 i, j, 2 k)

d e g 2 r a d [(x^{2} + 2) (x - 1)]^{^{'}}

e x p an d \frac{3 ( x + h ) + 7}{7 ( x + h ) - 8}

e x p an d \frac{3 ( 7 - 2 3 )}{37}

e x p an d (x + 1) ln (x) (1, e)