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

Lösung

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

4 x

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 4 x + 0 + 0

Vereinfache

= 4 x

\frac{d}{d x} (\frac{2 x + 1}{x - 3})

\frac{d}{d x} (sin (ln (3 x^{2} + x)))

\frac{d}{d x} (- \frac{10}{10 - x})

\int \frac{1}{x \cdot 1 - x ^{2}} d x

\frac{d}{d x} (a x e^{2 x})