derivative of (sin(x)/(1+tan(x)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

t an g e n t x + \frac{3}{x}, at x = 2

d er i v a t i v e f (x) = 4 - 2 x

x \to 2 lim (\frac{( x ^{6} - 64 )}{x - 2})

d er i v a t i v e f (x) = 2 x

\int \frac{1}{( s - 1 ) ^{2}} d s