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

Lösung

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

2 x

Schritte zur Lösung

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

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

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

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

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

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

\frac{\partial}{\partial x} (4) = 0

= 2 x - 0 + 0 - 0 - 0

Vereinfache

= 2 x

\int - 17 sin^{4} (x) cos (x) d x

d er i v a t i v e 5 x^{\frac{1}{3}} - 5 x^{- \frac{2}{3}}

d er i v a t i v e (x^{2} + 1)^{x}

in v erse l a pl a ce \frac{16}{s ( s ^{2} + 4 s + 16 )}

d er i v a t i v e \frac{1 - y}{x - 1}