(\partial)/(\partial x)(msin(2(mx+ny)))

Lösung

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

2 m^{2} cos (2 (m x + n y))

Schritte zur Lösung

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

Behandle

m, n, y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

= m cos (2 (m x + n y)) \cdot 2 m

Vereinfache

m cos (2 (m x + n y)) \cdot 2 m : 2 m^{2} cos (2 (m x + n y))

= 2 m^{2} cos (2 (m x + n y))

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

d er i v a t i v e f (x) = x (5 x^{5} - 1)

d er i v a t i v e 3 t^{2} + 5 t^{3}

\int x sin (9 x^{2}) d x

\frac{d}{d x} (\frac{x ^{6}}{6} + \frac{1}{16 x ^{4}})