derivative of ax+cot(ax)

Lösung

\frac{d}{d x} (a x + cot (a x))

- a cot^{2} (a x)

Schritte zur Lösung

\frac{d}{d x} (a x + cot (a x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (a x) + \frac{d}{d x} (cot (a x))

\frac{d}{d x} (a x) = a

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

= a - csc^{2} (a x) a

Vereinfache

a - csc^{2} (a x) a : - a cot^{2} (a x)

= - a cot^{2} (a x)

x \to - 4 + lim (\frac{- 4 x}{x + 4})

f (x) = 2 sin^{2} (x)

\frac{\partial}{\partial x} (7 y e^{x})

\frac{d y}{d x} = \frac{2 x + sec ^{2} ( x )}{2 y}, y (0) = - 7

\frac{d}{d x} (\frac{( 2 x ^{5} + 3 x ^{4} - x ^{3} + 2 )}{x ^{2}})