derivative of xcos(x-picos(x)+2sin(x))

Lösung

\frac{d}{d x} (x cos (x) - π cos (x) + 2 sin (x))

- x sin (x) + π sin (x) + 3 cos (x)

Schritte zur Lösung

\frac{d}{d x} (x cos (x) - π cos (x) + 2 sin (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x cos (x)) - \frac{d}{d x} (π cos (x)) + \frac{d}{d x} (2 sin (x))

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

\frac{d}{d x} (π cos (x)) = - π sin (x)

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

= cos (x) - x sin (x) - (- π sin (x)) + 2 cos (x)

Vereinfache

= - x sin (x) + π sin (x) + 3 cos (x)

6 y^{^{''}} + y^{^{'}} - y = 0

\int_{0}^{\frac{π}{3}} cos^{3} (x) d x

(x y^{2} + x^{3}) d x + (y^{3} + x^{2} y) d y = 0

\int \frac{1}{x ^{2} + 2 x} d x

\int (4 - 3 sin (2 x))^{4} cos (2 x) d x