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Beliebt Rechnen >

derivative log_{e}(1/(csc(x)))

Lösung

ableitung von

lo g_{e} (\frac{1}{csc ( x )})

Lösung

cot (x)

Schritte zur Lösung

\frac{d}{d x} (lo g_{e} (\frac{1}{csc ( x )}))

Vereinfache

lo g_{e} (\frac{1}{csc ( x )}) : ln (sin (x))

= \frac{d}{d x} (ln (sin (x)))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (sin (x)) = cos (x)

= \frac{1}{sin ( x )} cos (x)

Vereinfache

\frac{1}{sin ( x )} cos (x) : cot (x)

= cot (x)

Graph

Beliebte Beispiele

taylor (1+x)^{1/x}

t a y l or (1 + x)^{\frac{1}{x}}

y^{'''}+10y^{''}+25y^'=0

y^{^{'''}} + 10 y^{^{''}} + 25 y^{^{'}} = 0

(\partial)/(\partial x)(-2xy+x^3)

\frac{\partial}{\partial x} (- 2 x y + x^{3})

tangent f(x)=2-3x^2,\at x=-2

t an g e n t f (x) = 2 - 3 x^{2}, at x = - 2

(dy)/(dx)=y^2-2y

\frac{d y}{d x} = y^{2} - 2 y