derivative of sin^8(5x^2+8)

Lösung

\frac{d}{d x} (sin^{8} (5 x^{2} + 8))

80 x sin^{7} (5 x^{2} + 8) cos (5 x^{2} + 8)

Schritte zur Lösung

\frac{d}{d x} (sin^{8} (5 x^{2} + 8))

Wende die Kettenregel an:

8 (sin (5 x^{2} + 8))^{7} \frac{d}{d x} (sin (5 x^{2} + 8))

= 8 (sin (5 x^{2} + 8))^{7} \frac{d}{d x} (sin (5 x^{2} + 8))

\frac{d}{d x} (sin (5 x^{2} + 8)) = cos (5 x^{2} + 8) \cdot 10 x

= 8 (sin (5 x^{2} + 8))^{7} cos (5 x^{2} + 8) \cdot 10 x

Vereinfache

= 80 x sin^{7} (5 x^{2} + 8) cos (5 x^{2} + 8)

\int \frac{e ^{13 x}}{( e ^{13 x} + 5 ) ^{4}} d x

\frac{d y}{d x} - 0.11 y = 200

\frac{d}{d x} (\frac{x - 3}{2 x - 5})

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

d er i v a t i v e ln (x^{2} + 4) + x sin (2 x)