derivative of xcos(y-ycos(x))

Lösung

\frac{d}{d x} (x cos (y) - y cos (x))

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

Schritte zur Lösung

\frac{d}{d x} (x cos (y) - y cos (x))

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

t an g e n t y = 6 + 4 x^{2} - 2 x^{3}, at x = a

\int \frac{arcsin ( 7 x )}{1 - 49 x ^{2}} d x

\int \frac{1}{x ^{2} + 8 x} d x

x \to 1 lim (\frac{2 x + 1}{x + 2})

\frac{d}{d x} ((9 x^{2} - 3 x - 10) y^{^{''}} + (x^{2} + x) y^{^{'}} + (2 x - 1) y)