derivative of cos(xln(cos(x))+xsin(x))

Lösung

\frac{d}{d x} (cos (x) ln (cos (x)) + x sin (x))

x cos (x) - ln (cos (x)) sin (x)

Schritte zur Lösung

\frac{d}{d x} (cos (x) ln (cos (x)) + x sin (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (cos (x) ln (cos (x))) + \frac{d}{d x} (x sin (x))

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

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

= - sin (x) - ln (cos (x)) sin (x) + sin (x) + x cos (x)

Vereinfache

= x cos (x) - ln (cos (x)) sin (x)

\frac{d}{d x} (\frac{ln ( 4 x )}{4 x})

a re a y = 4 - x^{2}, y = x + 2

\frac{\partial}{\partial y} (\frac{1}{x y})

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

\int \frac{3}{x ^{2}} - \frac{2}{x ^{3}} d x