derivative of sqrt(sin(x-1(x^3)))

Lösung

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

\frac{x ( x cos ( x - 1 ) + 3 sin ( x - 1 ) )}{2 sin ( x - 1 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2 sin ( x - 1 ) x ^{3}} (cos (x - 1) x^{3} + 3 x^{2} sin (x - 1)) : \frac{x ( x cos ( x - 1 ) + 3 sin ( x - 1 ) )}{2 sin ( x - 1 )}

= \frac{x ( x cos ( x - 1 ) + 3 sin ( x - 1 ) )}{2 sin ( x - 1 )}

x \to 6 lim (9)

\frac{d y}{d t} + t^{2} y = 1

\frac{\partial}{\partial x} (e^{x} cos (y))

y^{^{'}} - \frac{2}{x ^{2}} y = 0

f (x) = 2 x^{2} ln (2 x)