derivative of sqrt(25-x^2-y^2)

Lösung

\frac{d}{d x} (25 - x^{2} - y^{2})

- \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 25}

Schritte zur Lösung

\frac{d}{d x} (25 - x^{2} - y^{2})

Wende die Kettenregel an:

\frac{1}{2 25 - x ^{2} - y ^{2}} \frac{d}{d x} (25 - x^{2} - y^{2})

= \frac{1}{2 25 - x ^{2} - y ^{2}} \frac{d}{d x} (25 - x^{2} - y^{2})

\frac{d}{d x} (25 - x^{2} - y^{2}) = - 2 x - 2 y \frac{d y}{d x}

= \frac{1}{2 25 - x ^{2} - y ^{2}} (- 2 x - 2 y \frac{d y}{d x})

Vereinfache

\frac{1}{2 25 - 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} + 25}

= - \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 25}

t an g e n t f (x) = \frac{x ^{2}}{x + 8}, (1, \frac{1}{9})

y^{^{'}} = y^{2} + 1

d er i v a t i v e f (x) = x 4 - x

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

x \to 2 π lim (\frac{sin ( x )}{x})