derivative ((x+8)/(x-8))^5

Lösung

ableitung von

(\frac{x + 8}{x - 8})^{5}

- \frac{80 ( x + 8 ) ^{4}}{( x - 8 ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x + 8}{x - 8})^{5})

Wende die Kettenregel an:

5 (\frac{x + 8}{x - 8})^{4} \frac{d}{d x} (\frac{x + 8}{x - 8})

= 5 (\frac{x + 8}{x - 8})^{4} \frac{d}{d x} (\frac{x + 8}{x - 8})

\frac{d}{d x} (\frac{x + 8}{x - 8}) = - \frac{16}{( x - 8 ) ^{2}}

= 5 (\frac{x + 8}{x - 8})^{4} (- \frac{16}{( x - 8 ) ^{2}})

Vereinfache

5 (\frac{x + 8}{x - 8})^{4} (- \frac{16}{( x - 8 ) ^{2}}) : - \frac{80 ( x + 8 ) ^{4}}{( x - 8 ) ^{6}}

= - \frac{80 ( x + 8 ) ^{4}}{( x - 8 ) ^{6}}

d er i v a t i v e e^{x} ln (x)

n = 1 \sum \infty \frac{1}{n ^{2} + 7 n}

d er i v a t i v e F (x) = (x^{4} + 9 x^{2} - 7)^{8}

\int_{3}^{9} \frac{8}{x} d x

x \to 4 lim (\frac{7 + x}{4 - x})