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

Lösung

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

- cot (x) csc (x) + sec (x) tan (x)

Schritte zur Lösung

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

Vereinfache

\frac{1}{sin ( x )} + \frac{1}{cos ( x )} : csc (x) + sec (x)

= \frac{d}{d x} (csc (x) + sec (x))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (csc (x)) + \frac{d}{d x} (sec (x))

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= - cot (x) csc (x) + sec (x) tan (x)

\frac{d}{d y} (2 4 - y)

\int \frac{5}{( x - 2 ) ^{2}} d x

\frac{d}{d x} (2 sec (x))

d er i v a t i v e y = 1 + e^{- 2 x^{2} + 8 x - 7}

x \to 0 lim (- (\frac{1}{x ^{2}}))