d/(dy)((x)(y^5-3xy))

Lösung

\frac{d}{d y} ((x) (y^{5} - 3 x y))

x (5 y^{4} - 3 x)

Schritte zur Lösung

\frac{d}{d y} ((x) (y^{5} - 3 x y))

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{d}{d y} (y^{5} - 3 x y)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= x (\frac{d}{d y} (y^{5}) - \frac{d}{d y} (3 x y))

\frac{d}{d y} (y^{5}) = 5 y^{4}

\frac{d}{d y} (3 x y) = 3 x

= x (5 y^{4} - 3 x)

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

e x p an d (e^{2 x}) (x^{2} + 9)

e x p an d \frac{d x}{( e ^{x} + 1 ) ^{3} e ^{- x}}

e x p an d \frac{[ x y ( 3 x ^{2} - 5 y ^{2} ) - x ^{4} + 3 y ^{4} ]}{( x - y ) ^{2}}

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