derivative arctan(cos(θ))

Lösung

ableitung von

arctan (cos (θ))

- \frac{sin ( θ )}{cos ^{2} ( θ ) + 1}

Schritte zur Lösung

\frac{d}{d θ} (arctan (cos (θ)))

Wende die Kettenregel an:

\frac{1}{( cos ( θ ) ) ^{2} + 1} \frac{d}{d θ} (cos (θ))

= \frac{1}{( cos ( θ ) ) ^{2} + 1} \frac{d}{d θ} (cos (θ))

\frac{d}{d θ} (cos (θ)) = - sin (θ)

= \frac{1}{( cos ( θ ) ) ^{2} + 1} (- sin (θ))

Vereinfache

\frac{1}{cos ^{2} ( θ ) + 1} (- sin (θ)) : - \frac{sin ( θ )}{cos ^{2} ( θ ) + 1}

= - \frac{sin ( θ )}{cos ^{2} ( θ ) + 1}

im pl i c i t \frac{d y}{d x}, y = \frac{- 5 x}{5} + 3 x^{3} - \frac{4}{5 x}

t an g e n t y = 3 x^{2} - 5 x + 9

y^{^{''}} + 9 y = 3 sec (3 x)

d er i v a t i v e 5 x e^{2 x}

x \to 0 lim (e^{x} + 2 x)