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Beliebt Rechnen >

derivative of (x^x/(sin(x)))

Lösung

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

Lösung

x^{x} csc (x) (ln (x) + 1) - x^{x} cot (x) csc (x)

Schritte zur Lösung

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

Vereinfache

\frac{x ^{x}}{sin ( x )} : x^{x} csc (x)

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

Wende die Produktregel an:

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

f = x^{x}, g = csc (x)

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

\frac{d}{d x} (x^{x}) = x^{x} (ln (x) + 1)

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

= x^{x} (ln (x) + 1) csc (x) + (- cot (x) csc (x)) x^{x}

Vereinfache

= x^{x} csc (x) (ln (x) + 1) - x^{x} cot (x) csc (x)

Graph

Beliebte Beispiele

(dy)/(dx)=k*y^2

\frac{d y}{d x} = k \cdot y^{2}

(dy)/(dx)= 1/(1+x)

\frac{d y}{d x} = \frac{1}{1 + x}

derivative f(x)=-12x^2+400x-3800

d er i v a t i v e f (x) = - 12 x^{2} + 400 x - 3800

tangent 3x-4x^2

t an g e n t 3 x - 4 x^{2}

integral of (1-sin^2(x))cos(x)

\int (1 - sin^{2} (x)) cos (x) d x