(\partial)/(\partial x)(x^2+y^2+z^2-1)

Lösung

\frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2} - 1)

2 x

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2} - 1)

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} (1)

\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} (1) = 0

= 2 x + 0 + 0 - 0

Vereinfache

= 2 x

ma c l a u r in arccos (\frac{cos ( x )}{1 + cos ( x )})

f (x) = sin (8 x)

d er i v a t i v e y = x^{9 c o s (x)}

\int 2 - ∣ x ∣ d x

\frac{d}{d x} ((x^{3} + x^{2} - 2) (7 + x - x^{4}))