derivative of sqrt(1+cos^2(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int (x - 2) e^{x} d x

d er i v a t i v e y = 2 arcsin (3) x^{5}

t an g e n t y = 5 - 7 x^{2}, (3, - 58)

\int \frac{5 sin ( x )}{cos ^{3} ( x )} d x

\int \frac{x ^{2}}{2} d x