derivative of sqrt(9-x^2-y^2)

Lösung

\frac{d}{d x} (9 - x^{2} - y^{2})

- \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 9}

Schritte zur Lösung

\frac{d}{d x} (9 - x^{2} - y^{2})

Wende die Kettenregel an:

\frac{1}{2 9 - x ^{2} - y ^{2}} \frac{d}{d x} (9 - x^{2} - y^{2})

= \frac{1}{2 9 - x ^{2} - y ^{2}} \frac{d}{d x} (9 - x^{2} - y^{2})

\frac{d}{d x} (9 - x^{2} - y^{2}) = - 2 x - 2 y \frac{d y}{d x}

= \frac{1}{2 9 - x ^{2} - y ^{2}} (- 2 x - 2 y \frac{d y}{d x})

Vereinfache

\frac{1}{2 9 - x ^{2} - y ^{2}} (- 2 x - 2 y \frac{d y}{d x}) : - \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 9}

= - \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 9}

d er i v a t i v e 6 u + 7 u

\frac{\partial}{\partial x} ((- (3 x + 9))^{9})

d er i v a t i v e f (x) = 5 x - 6 x^{2}

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

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