(\partial)/(\partial y)((x)(4x^2y+3y-5))

Lösung

\frac{\partial}{\partial y} ((x) (4 x^{2} y + 3 y - 5))

x (4 x^{2} + 3)

Schritte zur Lösung

\frac{\partial}{\partial y} ((x) (4 x^{2} y + 3 y - 5))

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{\partial}{\partial y} (4 x^{2} y + 3 y - 5)

Wende die Summen-/Differenzregel an:

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

= x (\frac{\partial}{\partial y} (4 x^{2} y) + \frac{\partial}{\partial y} (3 y) - \frac{\partial}{\partial y} (5))

\frac{\partial}{\partial y} (4 x^{2} y) = 4 x^{2}

\frac{\partial}{\partial y} (3 y) = 3

\frac{\partial}{\partial y} (5) = 0

= x (4 x^{2} + 3 - 0)

Vereinfache

= x (4 x^{2} + 3)

s im pl i f y (\frac{1}{s - 2} + 1) (s - 3)

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

e x p an d (20 b d z + 32 c g a) + k (20 b d z + 32 c g a)

e x p an d (\frac{b}{a} (x - z) + y - c)^{2}

e x p an d 2 (e - 1) + \frac{e ^{6} + e ^{2} - 2}{4 e ^{2}}