derivative of ((x+2/(x-2))^2)

Lösung

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

- \frac{8 ( x + 2 )}{( x - 2 ) ^{3}}

Schritte zur Lösung

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

Wende die Kettenregel an:

2 \cdot \frac{x + 2}{x - 2} \frac{d}{d x} (\frac{x + 2}{x - 2})

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

\frac{d}{d x} (\frac{x + 2}{x - 2}) = - \frac{4}{( x - 2 ) ^{2}}

= 2 \cdot \frac{x + 2}{x - 2} (- \frac{4}{( x - 2 ) ^{2}})

Vereinfache

2 \cdot \frac{x + 2}{x - 2} (- \frac{4}{( x - 2 ) ^{2}}) : - \frac{8 ( x + 2 )}{( x - 2 ) ^{3}}

= - \frac{8 ( x + 2 )}{( x - 2 ) ^{3}}

\int (x - x + 1) (x + 1) d x

12 x^{3} - 3 y^{2} x^{4} + 1 \frac{d y}{d x} = 0

\frac{\partial}{\partial x} (cos^{5} (x^{3} y^{8}))

\frac{d ^{2} y}{d x ^{2}} = - y

d er i v a t i v e f (x) = x^{2} (3 - x)^{2}