derivative of sin^3(4x^2-1)

Lösung

\frac{d}{d x} (sin^{3} (4 x^{2} - 1))

24 x sin^{2} (4 x^{2} - 1) cos (4 x^{2} - 1)

Schritte zur Lösung

\frac{d}{d x} (sin^{3} (4 x^{2} - 1))

Wende die Kettenregel an:

3 (sin (4 x^{2} - 1))^{2} \frac{d}{d x} (sin (4 x^{2} - 1))

= 3 (sin (4 x^{2} - 1))^{2} \frac{d}{d x} (sin (4 x^{2} - 1))

\frac{d}{d x} (sin (4 x^{2} - 1)) = cos (4 x^{2} - 1) \cdot 8 x

= 3 (sin (4 x^{2} - 1))^{2} cos (4 x^{2} - 1) \cdot 8 x

Vereinfache

= 24 x sin^{2} (4 x^{2} - 1) cos (4 x^{2} - 1)

x \to \frac{π}{2} lim (ln (sin (x)))

a re a \frac{2}{x}, 8 x, \frac{1}{2} x

x \to 3 lim (2 - x)

\frac{d}{d x} (\frac{1 - cos ( x )}{1 + sin ( x )})

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