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Beliebt Rechnen >

(\partial)/(\partial y)((sin(mx+ny))^2)

Lösung

\frac{\partial}{\partial y} ((sin (m x + n y))^{2})

Lösung

n sin (2 (m x + n y))

Schritte zur Lösung

\frac{\partial}{\partial y} ((sin (m x + n y))^{2})

Behandle

n, m, x

als Konstanten

Wende die Kettenregel an:

2 sin (m x + n y) \frac{\partial}{\partial y} (sin (m x + n y))

= 2 sin (m x + n y) \frac{\partial}{\partial y} (sin (m x + n y))

\frac{\partial}{\partial y} (sin (m x + n y)) = cos (m x + n y) n

= 2 sin (m x + n y) cos (m x + n y) n

Verwende die Doppelwinkelidentität:

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

= n sin (2 (m x + n y))

Beliebte Beispiele

integral of 2e^{-x^2}

\int 2 e^{- x^{2}} d x

derivative of 1/6 (2x+1^3)

\frac{d}{d x} (\frac{1}{6} (2 x + 1)^{3})

derivative of (x-sqrt(x)/(x^{1/4)})

\frac{d}{d x} (\frac{x - x}{x ^{\frac{1}{4}}})

limit as x approaches-2 of (5x+7)^4

x \to - 2 lim ((5 x + 7)^{4})

derivative 2^{x^2-3}

d er i v a t i v e 2^{x^{2} - 3}