derivative of sin(xx^{-2})

Lösung

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

\frac{cos ( x )}{x ^{2}} - \frac{2 sin ( x )}{x ^{3}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (x^{- 2}) = - \frac{2}{x ^{3}}

= cos (x) x^{- 2} + (- \frac{2}{x ^{3}}) sin (x)

Vereinfache

cos (x) x^{- 2} + (- \frac{2}{x ^{3}}) sin (x) : \frac{cos ( x )}{x ^{2}} - \frac{2 sin ( x )}{x ^{3}}

= \frac{cos ( x )}{x ^{2}} - \frac{2 sin ( x )}{x ^{3}}

\int e^{- n x} d x

(x \frac{d y}{d x} + 2 y) = 3

t an g e n t f (x) = 9 - x, at x = 2

y^{^{'}} = e^{8 x + y}

\frac{\partial}{\partial y} (z e^{x y})