(\partial)/(\partial x)(x^4+2y^6-xy-x+2)

Lösung

\frac{\partial}{\partial x} (x^{4} + 2 y^{6} - x y - x + 2)

4 x^{3} - y - 1

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{4} + 2 y^{6} - x y - x + 2)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{4}) + \frac{\partial}{\partial x} (2 y^{6}) - \frac{\partial}{\partial x} (x y) - \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (2)

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

\frac{\partial}{\partial x} (2 y^{6}) = 0

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

\frac{\partial}{\partial x} (x) = 1

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

= 4 x^{3} + 0 - y - 1 + 0

Vereinfache

= 4 x^{3} - y - 1

\int_{0}^{4} π (x + 1)^{2} d x

d er i v a t i v e f (x) = x^{3} + 2 x - 3

t an g e n t x^{2} + y^{2} = 50, (7, - 1)

x \to + (- 7) lim (- 13)

x \to \infty lim (3 x^{2})