derivative (-cos(x))/(sin^2(x))

Lösung

ableitung von

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

- csc (x) + 2 csc^{3} (x)

Schritte zur Lösung

\frac{d}{d x} (\frac{- cos ( x )}{sin ^{2} ( x )})

Vereinfache

\frac{- cos ( x )}{sin ^{2} ( x )} : - cot (x) csc (x)

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cot (x), g = csc (x)

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

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

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

= - ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x))

Vereinfache

- ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x)) : - csc (x) + 2 csc^{3} (x)

= - csc (x) + 2 csc^{3} (x)

d er i v a t i v e (lo g_{10} (x^{3} + 4))^{5}

d er i v a t i v e e^{c o s^{2} (x)}

d er i v a t i v e - 2 sin^{2} (x)

d er i v a t i v e \frac{1}{( x ^{2} + x )}

d er i v a t i v e (x + 3)^{\frac{1}{2}}