derivative of x^2*(sin(x)^{-1})

Lösung

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

\frac{2 x - x ^{2} cot ( x )}{sin ( x )}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = (sin (x))^{- 1}

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

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

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

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

Vereinfache

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

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

\int (\frac{1}{( 1 + 4 x ^{2} ) ( arctan ( 2 x ) ) ^{3}}) d x

\int \frac{( 2 x + 3 )}{( x + 7 ) ^{3}} d x

n = 1 \sum \infty 3 (\frac{1}{5})^{n - 1}

d er i v a t i v e f (x) = e^{2 x} - 1

n = 1 \sum \infty - n