derivative f(x)=(cos(x))/(1+asin(x))

Lösung

ableitung von

f (x) = \frac{cos ( x )}{1 + a sin ( x )}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

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

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

d er i v a t i v e y = sin (ln (x))

\frac{d x}{d t} = cot (x) cos (t)

d er i v a t i v e (x + 1) e^{x}

x \to 0 lim (sin (x) ln (4 x))

\int \frac{I n ( x + 1 )}{x + 1} d x