derivative of ((x^2+2/(x^2-2))^8)

Lösung

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

- \frac{64 x ( x ^{2} + 2 ) ^{7}}{( x ^{2} - 2 ) ^{9}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

= 8 (\frac{x ^{2} + 2}{x ^{2} - 2})^{7} \frac{d}{d x} (\frac{x ^{2} + 2}{x ^{2} - 2})

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

= 8 (\frac{x ^{2} + 2}{x ^{2} - 2})^{7} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}})

Vereinfache

8 (\frac{x ^{2} + 2}{x ^{2} - 2})^{7} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}}) : - \frac{64 x ( x ^{2} + 2 ) ^{7}}{( x ^{2} - 2 ) ^{9}}

= - \frac{64 x ( x ^{2} + 2 ) ^{7}}{( x ^{2} - 2 ) ^{9}}

s l o p e (- 4, 2), (4, - 2)

t an g e n t f (x) = \frac{x ^{3}}{2}, at x = - 6

\int \frac{sin ( 2 x )}{1} d x

a re a x^{2}, x^{4}

y^{^{''}} + y^{^{'}} + 36 y = 6 sin (6 t)