derivative of sin(x+4/9 cot(x))

Lösung

\frac{d}{d x} (sin (x) + \frac{4}{9} cot (x))

cos (x) - \frac{4}{9} csc^{2} (x)

Schritte zur Lösung

\frac{d}{d x} (sin (x) + \frac{4}{9} cot (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (sin (x)) + \frac{d}{d x} (\frac{4}{9} cot (x))

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

\frac{d}{d x} (\frac{4}{9} cot (x)) = - \frac{4}{9} csc^{2} (x)

= cos (x) - \frac{4}{9} csc^{2} (x)

x \to 1 lim (F (x))

\int 3 (csc (x))^{2} cot^{3} (x) d x

\int 2 cos (4 x) e^{s i n (4 x)} d x

d er i v a t i v e 2 n d

t an g e n t f (x) = \frac{1 + 2 x}{3 + x}, at x = 2