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Beliebt Rechnen >

derivative of sin^2(ax)

Lösung

\frac{d}{d x} (sin^{2} (a x))

Lösung

a sin (2 a x)

Schritte zur Lösung

\frac{d}{d x} (sin^{2} (a x))

Wende die Kettenregel an:

2 sin (a x) \frac{d}{d x} (sin (a x))

= 2 sin (a x) \frac{d}{d x} (sin (a x))

\frac{d}{d x} (sin (a x)) = cos (a x) a

= 2 sin (a x) cos (a x) a

Verwende die Doppelwinkelidentität:

2 sin (x) cos (x) = sin (2 x)

= a sin (2 a x)

Graph

Beliebte Beispiele

derivative of (x^2/(5+2x))

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

integral of x/(sqrt(3x^2+5))

\int \frac{x}{3 x ^{2} + 5} d x

derivative of 4/((x+2^2+16))

\frac{d}{d x} (\frac{4}{( x + 2 ) ^{2} + 16})

(\partial)/(\partial x)((e^x-x)cos(y))

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

\frac{d}{d t} (- 32 t)