derivative sqrt(x)csc(x)

Lösung

ableitung von

x csc (x)

\frac{csc ( x )}{2 x} - x cot (x) csc (x)

Schritte zur Lösung

\frac{d}{d x} (x csc (x))

Wende die Produktregel an:

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

f = x, g = csc (x)

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= \frac{1}{2 x} csc (x) + (- cot (x) csc (x)) x

Vereinfache

\frac{1}{2 x} csc (x) + (- cot (x) csc (x)) x : \frac{csc ( x )}{2 x} - x cot (x) csc (x)

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

xx y^{^{'}} = y^{2} + 1

5 y^{^{''}} + 25 y^{^{'}} + 1700 y = 0

\int \frac{1}{x ^{2}} 7 + \frac{1}{x} d x

\frac{d}{d x} (x^{4} - 5 x)

d er i v a t i v e 2 cos (x) - 2 sin (x)