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Beliebt Rechnen >

derivative of 1/x-1/(sin(x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

\frac{1}{x} - \frac{1}{sin ( x )} : \frac{1}{x} - csc (x)

= \frac{d}{d x} (\frac{1}{x} - csc (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{1}{x}) - \frac{d}{d x} (csc (x))

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

(dy)/(dx)=(6x^4e^{y/x}+x^2y^2)/(x^3y)

\frac{d y}{d x} = \frac{6 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

limit as x approaches 0+of sqrt(-x)

x \to 0 + lim (- x)

integral of sec(x)tan(x)-6e^x

\int sec (x) tan (x) - 6 e^{x} d x

y^{^{'}} = 5 (y - t^{2})

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