derivative ((x+7)/(x-7))^5

Lösung

ableitung von

(\frac{x + 7}{x - 7})^{5}

- \frac{70 ( x + 7 ) ^{4}}{( x - 7 ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x + 7}{x - 7})^{5})

Wende die Kettenregel an:

5 (\frac{x + 7}{x - 7})^{4} \frac{d}{d x} (\frac{x + 7}{x - 7})

= 5 (\frac{x + 7}{x - 7})^{4} \frac{d}{d x} (\frac{x + 7}{x - 7})

\frac{d}{d x} (\frac{x + 7}{x - 7}) = - \frac{14}{( x - 7 ) ^{2}}

= 5 (\frac{x + 7}{x - 7})^{4} (- \frac{14}{( x - 7 ) ^{2}})

Vereinfache

5 (\frac{x + 7}{x - 7})^{4} (- \frac{14}{( x - 7 ) ^{2}}) : - \frac{70 ( x + 7 ) ^{4}}{( x - 7 ) ^{6}}

= - \frac{70 ( x + 7 ) ^{4}}{( x - 7 ) ^{6}}

y^{^{'}} + (\frac{3}{300 - x}) y = 4

t a y l or f (x) = ln (1 + x)

\int \frac{( 5 + ln ( x ) ) ^{\frac{2}{3}}}{x} d x

\frac{\partial}{\partial y} (x^{5 y})

\int (x^{5}) d x