derivative y=(sin(2x^3-1))^2

Lösung

ableitung von

y = (sin (2 x^{3} - 1))^{2}

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (sin (2 x^{3} - 1)) = cos (2 x^{3} - 1) \cdot 6 x^{2}

= 2 sin (2 x^{3} - 1) cos (2 x^{3} - 1) \cdot 6 x^{2}

Vereinfache

= 12 x^{2} sin (2 x^{3} - 1) cos (2 x^{3} - 1)

\int_{1}^{3} 19 r^{3} ln (r) d r

d er i v a t i v e y = \frac{5}{( 2 x ^{3} )} + 2 cos (x)

\frac{d}{d x} (4 cos (5 x))

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

\int \frac{2 x + 4}{x ^{2} + 5 x - 6} d x