(\partial)/(\partial x)((x)(x-3)(y-4))

Lösung

\frac{\partial}{\partial x} ((x) (x - 3) (y - 4))

(y - 4) (2 x - 3)

Schritte zur Lösung

\frac{\partial}{\partial x} ((x) (x - 3) (y - 4))

Behandle

y

als Konstante

Entferne die Konstante:

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

= (y - 4) \frac{\partial}{\partial x} (x (x - 3))

Wende die Produktregel an:

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

f = x, g = x - 3

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (x - 3) = 1

= (y - 4) (1 \cdot (x - 3) + 1 \cdot x)

Vereinfache

(y - 4) (1 \cdot (x - 3) + 1 \cdot x) : (y - 4) (2 x - 3)

= (y - 4) (2 x - 3)

e x p an d f (x) x (2 (y)^{''} - x (y)^{'} = e^{- x})

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

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

e x p an d (x + sin (x) - 1)^{2}

e x p an d (2 x) (3 x + 1 + 1)