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Beliebt Rechnen >

derivative of ((x^2)/(sin(x)))

Lösung

\frac{d}{d x} (\frac{( x ^{2} )}{sin ( x )})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{( x ^{2} )}{sin ( x )})

Vereinfache

\frac{( x ^{2} )}{sin ( x )} : x^{2} csc (x)

= \frac{d}{d x} (x^{2} csc (x))

Wende die Produktregel an:

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

f = x^{2}, g = csc (x)

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

integral of x(x+1)^4

y^{''}-9y=e^{3x}

derivative of {y}(θ,xtan(θ))