(\partial)/(\partial x)(4cos^3(kx-wt)-3cos(kx-wt))

Lösung

\frac{\partial}{\partial x} (4 cos^{3} (k x - wt) - 3 cos (k x - wt))

- 12 k cos^{2} (k x - wt) sin (k x - wt) + 3 k sin (k x - wt)

Schritte zur Lösung

\frac{\partial}{\partial x} (4 cos^{3} (k x - wt) - 3 cos (k x - wt))

Behandle

k, w, t

als Konstanten

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (4 cos^{3} (k x - wt)) - \frac{\partial}{\partial x} (3 cos (k x - wt))

\frac{\partial}{\partial x} (4 cos^{3} (k x - wt)) = - 12 k cos^{2} (k x - wt) sin (k x - wt)

\frac{\partial}{\partial x} (3 cos (k x - wt)) = - 3 k sin (k x - wt)

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

Vereinfache

= - 12 k cos^{2} (k x - wt) sin (k x - wt) + 3 k sin (k x - wt)

t an g e n t sin (5 x) + cos (2 x)

\int e^{15 x} d x

\int tan^{3} (5 x) sec^{5} (5 x) d x

\frac{d}{d x} ((6 x^{2} + 8)^{6})

\int_{0}^{3} - x^{2} + 3 x d x