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

Lösung

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

2 x

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (4 y^{2}) = 0

\frac{\partial}{\partial x} (5 z^{2}) = 0

= 2 x + 0 + 0

Vereinfache

= 2 x

f (x) = \frac{7}{10} x^{2} + 4 x^{3}

\frac{d p}{p - p ^{2}} = d t

\frac{d}{d x} (3 x^{4} + 2 x^{3} + x^{2} - 2)

\frac{d ^{2}}{d x ^{2}} (x^{- 2})

\frac{d y}{d x} = - \frac{y ( x + y + 1 )}{x + 2 y}