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

Lösung

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

z (8 x + 3)

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

\frac{\partial}{\partial x} (3 y^{2}) = 0

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

= z (8 x + 0 + 3)

Vereinfache

= z (8 x + 3)

s im pl i f y (- 3 + i)^{10}

e x p an d \frac{( x - 4 ) ( x - 1 ) ( x + 3 )}{( x - 3 ) ( x + 2 )}

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

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

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