(\partial)/(\partial x)((z)(x^2e^y+10y))

Lösung

\frac{\partial}{\partial x} ((z) (x^{2} e^{y} + 10 y))

2 e^{y} z x

Schritte zur Lösung

\frac{\partial}{\partial x} ((z) (x^{2} e^{y} + 10 y))

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

= z \frac{\partial}{\partial x} (x^{2} e^{y} + 10 y)

Wende die Summen-/Differenzregel an:

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

= z (\frac{\partial}{\partial x} (x^{2} e^{y}) + \frac{\partial}{\partial x} (10 y))

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

\frac{\partial}{\partial x} (10 y) = 0

= z (2 e^{y} x + 0)

Vereinfache

= 2 e^{y} z x

e x p an d \frac{4 ( 6 + 3 )}{33}

s im pl i f y - 2 (2 + 34)

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

e x p an d \frac{( 2 x ^{3} - 4 x ^{2} - 15 x + 4 )}{( x - 1 ) ^{2}}

e x p an d (t^{2} e^{- t} - 4 t e^{- t} + 2 e^{- t})^{2} e^{t}