derivative cos^3(sin(2x^4-x))

Lösung

ableitung von

cos^{3} (sin (2 x^{4} - x))

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

a re a y = x^{2} - 7, y = 9

\frac{d}{d x} (- 3 \cdot e^{x^{2} + x - 1})

\frac{\partial}{\partial x} (- ln (1 + e^{- x}))

d er i v a t i v e f (w) = (6 x - 8)^{2}

d er i v a t i v e f (x) = 7 arctan (x - 1 + x^{2})