derivative f(x)=((x+2)/(x-2))^5

Lösung

ableitung von

f (x) = (\frac{x + 2}{x - 2})^{5}

- \frac{20 ( x + 2 ) ^{4}}{( x - 2 ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x + 2}{x - 2})^{5})

Wende die Kettenregel an:

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

= 5 (\frac{x + 2}{x - 2})^{4} \frac{d}{d x} (\frac{x + 2}{x - 2})

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

= 5 (\frac{x + 2}{x - 2})^{4} (- \frac{4}{( x - 2 ) ^{2}})

Vereinfache

5 (\frac{x + 2}{x - 2})^{4} (- \frac{4}{( x - 2 ) ^{2}}) : - \frac{20 ( x + 2 ) ^{4}}{( x - 2 ) ^{6}}

= - \frac{20 ( x + 2 ) ^{4}}{( x - 2 ) ^{6}}

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

\frac{\partial}{\partial x} (3 x e^{x^{2} + y^{2}})

\int \frac{cos ( x )}{sin ^{2} ( x ) - 49} d x

\frac{d}{d x} (tan^{2} (x^{2} - 5 x))

x \to 0 lim (\frac{8}{6 + e ^{x}})