derivative of arctan(cos(x))

Lösung

\frac{d}{d x} (arctan (cos (x)))

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

Schritte zur Lösung

\frac{d}{d x} (arctan (cos (x)))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int_{0}^{4} ∣ 3 t - 8 ∣ d t

d er i v a t i v e f (x) = \frac{4 x ^{2} - x + 3}{x}

\int \frac{e ^{- s t}}{- s} d t

\int (e^{c o s (x)} sin (x)) d x

\frac{d}{d x} (cos^{s i n (x)} (x))