derivative of sqrt(r^2-x^2)

Lösung

\frac{d}{d x} (r (x)^{2} - x^{2})

\frac{r \frac{d r}{d x} - x}{r ^{2} - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (r^{2} - x^{2})

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2 r ^{2} - x ^{2}} (2 r \frac{d r}{d x} - 2 x) : \frac{r \frac{d r}{d x} - x}{r ^{2} - x ^{2}}

= \frac{r \frac{d r}{d x} - x}{r ^{2} - x ^{2}}

\frac{\partial}{\partial x} (1 0^{x^{2} + x})

\frac{d}{d x} (\frac{1}{2 x + 3})

d er i v a t i v e x^{2} \cdot cos (x)

\frac{d}{d x} (\frac{x ^{3}}{3} - \frac{1}{4 x})

\frac{d}{d x} (- 0.5 x)