derivative of sin^{12}(3x^4-x)

Lösung

\frac{d}{d x} (sin^{12} (3 x^{4} - x))

12 sin^{11} (3 x^{4} - x) cos (3 x^{4} - x) (12 x^{3} - 1)

Schritte zur Lösung

\frac{d}{d x} (sin^{12} (3 x^{4} - x))

Wende die Kettenregel an:

12 (sin (3 x^{4} - x))^{11} \frac{d}{d x} (sin (3 x^{4} - x))

= 12 (sin (3 x^{4} - x))^{11} \frac{d}{d x} (sin (3 x^{4} - x))

\frac{d}{d x} (sin (3 x^{4} - x)) = cos (3 x^{4} - x) (12 x^{3} - 1)

= 12 (sin (3 x^{4} - x))^{11} cos (3 x^{4} - x) (12 x^{3} - 1)

Vereinfache

= 12 sin^{11} (3 x^{4} - x) cos (3 x^{4} - x) (12 x^{3} - 1)

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

l a pl a ce t r an s f or m 3 t^{2} - 9 t

d er i v a t i v e (4 x + 5)^{\frac{1}{5}}

d er i v a t i v e arccos (\frac{x}{5})

\int \frac{4 x}{x ^{2} + 5} d x