derivative y=xsin(2/x)

Lösung

ableitung von

y = x sin (\frac{2}{x})

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = sin (\frac{2}{x})

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

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

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

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

Vereinfache

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

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

t^{2} y^{^{''}} - 2 t y^{^{'}} + 2 y = t ln (t)

t an g e n t x^{2} + x y + y^{2} = 7, (2, 1)

\frac{d}{d x} (4 x^{5} - 3 x^{m} + 2 x^{n} + 5 x^{2} - x - 6)

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

\int 3 4 x^{3} - 8 x^{5} + 6 e^{x} - 2 d x