(\partial)/(\partial x)(x^2(x-y)^{-2})

Lösung

\frac{\partial}{\partial x} (x^{2} (x - y)^{- 2})

- \frac{2 x y}{( x - y ) ^{3}}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} (x - y)^{- 2})

Behandle

y

als Konstante

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

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

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

\int x^{2} sin (y) d y

\int sin (6 x) ln (sin (6 x)) d x

\int \frac{x ^{2}}{( 36 - x ^{2} ) ^{\frac{3}{2}}} d x