derivative f(x)=sin(sqrt(1+cos(x)))

Lösung

ableitung von

f (x) = sin (1 + cos (x))

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

Schritte zur Lösung

\frac{d}{d x} (sin (1 + cos (x)))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int_{0}^{1} \frac{14}{4 y - 1} d y

\frac{d}{d p} (ln (p))

\int x x - 3 d x

\int x^{2} 5 x + 7 d x

\frac{d}{d x} (\frac{6 x}{x ^{2} + 9})