derivative of sqrt(r^2-8x^2)

Lösung

\frac{d}{d x} (r (x)^{2} - 8 x^{2})

\frac{r \frac{d r}{d x} - 8 x}{r ^{2} - 8 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (r^{2} - 8 x^{2})

Wende die Kettenregel an:

\frac{1}{2 r ^{2} - 8 x ^{2}} \frac{d}{d x} (r^{2} - 8 x^{2})

= \frac{1}{2 r ^{2} - 8 x ^{2}} \frac{d}{d x} (r^{2} - 8 x^{2})

\frac{d}{d x} (r^{2} - 8 x^{2}) = 2 r \frac{d r}{d x} - 16 x

= \frac{1}{2 r ^{2} - 8 x ^{2}} (2 r \frac{d r}{d x} - 16 x)

Vereinfache

\frac{1}{2 r ^{2} - 8 x ^{2}} (2 r \frac{d r}{d x} - 16 x) : \frac{r \frac{d r}{d x} - 8 x}{r ^{2} - 8 x ^{2}}

= \frac{r \frac{d r}{d x} - 8 x}{r ^{2} - 8 x ^{2}}

\int x (x + 4)^{- \frac{3}{2}} d x

n = 1 \sum \infty (- 1)^{n} n^{- 3}

\int \frac{1}{x ^{2} x ^{2} - 81} d x

\int_{- 1}^{3} (- x^{3} + 3 x^{2} + 1) d x

im pl i c i t \frac{- 8 x}{y} = 0