derivative of y^2-x^3+8

Lösung

\frac{d}{d x} (y^{2} - x^{3} + 8)

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

Schritte zur Lösung

\frac{d}{d x} (y^{2} - x^{3} + 8)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (y^{2}) - \frac{d}{d x} (x^{3}) + \frac{d}{d x} (8)

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

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

\frac{d}{d x} (8) = 0

= 2 y \frac{d y}{d x} - 3 x^{2} + 0

Vereinfache

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

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

T \to 0 lim (a T + b)

t an g e n t f (x) = \frac{2}{2 x + 3 ^{2}}, at x = - \frac{1}{3}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 6 y = 10 e^{2 x} + 6 x + 7

\frac{d}{d x} (4 x^{2} + 5 x)