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

Lösung

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

2 x sin (\frac{2 π}{x}) - 2 π cos (\frac{2 π}{x})

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = sin (\frac{2 π}{x})

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

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

\frac{d}{d x} (sin (\frac{2 π}{x})) = - \frac{2 π cos ( \frac{2 π}{x} )}{x ^{2}}

= 2 x sin (\frac{2 π}{x}) + (- \frac{2 π cos ( \frac{2 π}{x} )}{x ^{2}}) x^{2}

Vereinfache

2 x sin (\frac{2 π}{x}) + (- \frac{2 π cos ( \frac{2 π}{x} )}{x ^{2}}) x^{2} : 2 x sin (\frac{2 π}{x}) - 2 π cos (\frac{2 π}{x})

= 2 x sin (\frac{2 π}{x}) - 2 π cos (\frac{2 π}{x})

\int x^{-} d x

d er i v a t i v e \frac{130700}{333 - v}

\int tan^{4} (\frac{3}{5} b x) d x

\int tan^{2} (\frac{x}{2}) d x

d er i v a t i v e h (- x) = \frac{x ^{2} + 9}{10}