(\partial)/(\partial x)(x^3+4x^2y+4x+2)

Lösung

\frac{\partial}{\partial x} (x^{3} + 4 x^{2} y + 4 x + 2)

3 x^{2} + 8 x y + 4

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{3} + 4 x^{2} y + 4 x + 2)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{3}) + \frac{\partial}{\partial x} (4 x^{2} y) + \frac{\partial}{\partial x} (4 x) + \frac{\partial}{\partial x} (2)

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

\frac{\partial}{\partial x} (4 x^{2} y) = 8 y x

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

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

= 3 x^{2} + 8 y x + 4 + 0

Vereinfache

= 3 x^{2} + 8 x y + 4

x \to 2 - lim (\frac{2}{2 - x})

x \to 0 lim (2 - x^{2})

d er i v a t i v e (1 + w) w^{3} + 9

d er i v a t i v e y = \frac{5 x}{x}

y^{^{''}} + y = 0.75 sin (t) - 0.25 sin (3 t)