derivative of cos(x-y+ln(x+y))

Lösung

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

- sin (x - y) (1 - \frac{d y}{d x}) + \frac{1 + \frac{d y}{d x}}{x + y}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (cos (x - y)) = - sin (x - y) (1 - \frac{d y}{d x})

\frac{d}{d x} (ln (x + y)) = \frac{1 + \frac{d y}{d x}}{x + y}

= - sin (x - y) (1 - \frac{d y}{d x}) + \frac{1 + \frac{d y}{d x}}{x + y}

\int \frac{2 x ^{3} - x ^{2} + 2 x + 4}{1 + x ^{2}} d x

\int (8 x + 3) 4 x^{2} + 3 x d x

\frac{d}{d x} (\frac{x ^{2} + 13 x + 36}{x ^{2} + 8 x - 9})

d er i v a t i v e 9 x^{\frac{2}{3}}

t an g e n t f (x) = 6 sec (x)