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Beliebt Rechnen >

derivative csc(x)(x+cot(x))

Lösung

ableitung von

csc (x) (x + cot (x))

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative e^{-x^2}

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

integral from 0 to sin(x) of 6sqrt(t)

\int_{0}^{s i n (x)} 6 t d t

y^{''}+2y^'-48y=0

y^{^{''}} + 2 y^{^{'}} - 48 y = 0

integral of u/u

\int \frac{u}{u} d u

tangent f(x)= 1/x+4,(-2,8)

t an g e n t f (x) = \frac{1}{x} + 4, (- 2, 8)