derivative of sqrt(r^2-7x^2)

Lösung

\frac{d}{d x} (r (x)^{2} - 7 x^{2})

\frac{r \frac{d r}{d x} - 7 x}{r ^{2} - 7 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (r^{2} - 7 x^{2})

Wende die Kettenregel an:

\frac{1}{2 r ^{2} - 7 x ^{2}} \frac{d}{d x} (r^{2} - 7 x^{2})

= \frac{1}{2 r ^{2} - 7 x ^{2}} \frac{d}{d x} (r^{2} - 7 x^{2})

\frac{d}{d x} (r^{2} - 7 x^{2}) = 2 r \frac{d r}{d x} - 14 x

= \frac{1}{2 r ^{2} - 7 x ^{2}} (2 r \frac{d r}{d x} - 14 x)

Vereinfache

\frac{1}{2 r ^{2} - 7 x ^{2}} (2 r \frac{d r}{d x} - 14 x) : \frac{r \frac{d r}{d x} - 7 x}{r ^{2} - 7 x ^{2}}

= \frac{r \frac{d r}{d x} - 7 x}{r ^{2} - 7 x ^{2}}

\frac{d}{d x} (2 sec^{2} (x) tan (x))

x \to 0 lim (\frac{5}{x - 1})

l a pl a ce t r an s f or m sin (2 t + 3)

a re a y = x, x \geq 0

\int \frac{1}{x 5 x ^{2} - 3} d x