d/(da)((sin(a)+cos(a))/(sec(a)+csc(a)))

Lösung

\frac{d}{d a} (\frac{sin ( a ) + cos ( a )}{sec ( a ) + csc ( a )})

\frac{( cos ( a ) - sin ( a ) ) ( sec ( a ) + csc ( a ) ) - ( sec ( a ) tan ( a ) - cot ( a ) csc ( a ) ) ( sin ( a ) + cos ( a ) )}{( sec ( a ) + csc ( a ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d a} (\frac{sin ( a ) + cos ( a )}{sec ( a ) + csc ( a )})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d a} ( sin ( a ) + cos ( a ) ) ( sec ( a ) + csc ( a ) ) - \frac{d}{d a} ( sec ( a ) + csc ( a ) ) ( sin ( a ) + cos ( a ) )}{( sec ( a ) + csc ( a ) ) ^{2}}

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

\frac{d}{d a} (sec (a) + csc (a)) = sec (a) tan (a) - cot (a) csc (a)

= \frac{( cos ( a ) - sin ( a ) ) ( sec ( a ) + csc ( a ) ) - ( sec ( a ) tan ( a ) - cot ( a ) csc ( a ) ) ( sin ( a ) + cos ( a ) )}{( sec ( a ) + csc ( a ) ) ^{2}}

\frac{d}{d x} (10 sin (2 x))

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

\frac{d}{d x} (x^{l o g_{6} (x)})

\int - 6 cos (x) d x

\int 11 ln (x^{2} - x + 2) d x