derivative of x^3-xy+cos(pi(x+y))

Lösung

\frac{d}{d x} (x^{3} - x y + cos (π) (x + y))

3 x^{2} - y - x \frac{d y}{d x} - 1 - \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (x^{3} - x y + cos (π) (x + y))

Vereinfache

x^{3} - x y + cos (π) (x + y) : x^{3} - x y - x - y

= \frac{d}{d x} (x^{3} - x y - x - y)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (x y) - \frac{d x}{d x} - \frac{d y}{d x}

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

\frac{d x}{d x} = 1

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

Vereinfache

= 3 x^{2} - y - x \frac{d y}{d x} - 1 - \frac{d y}{d x}

e x t re m e f (x, y) = 4 x^{2} - x y

e x t re m e f (x, y) = x + y + \frac{81}{x y}

e x t re m e f (x) = 2 (y + 1)^{2} + y^{2} - 2 y - 2

e x t re m e f (x) = x e^{\frac{x}{2}}, - 3 \leq x \leq 1

e x t re m e x + y - x y