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Beliebt Rechnen >

derivative ((x+6)/(x-6))^5

Lösung

ableitung von

(\frac{x + 6}{x - 6})^{5}

Lösung

- \frac{60 ( x + 6 ) ^{4}}{( x - 6 ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x + 6}{x - 6})^{5})

Wende die Kettenregel an:

5 (\frac{x + 6}{x - 6})^{4} \frac{d}{d x} (\frac{x + 6}{x - 6})

= 5 (\frac{x + 6}{x - 6})^{4} \frac{d}{d x} (\frac{x + 6}{x - 6})

\frac{d}{d x} (\frac{x + 6}{x - 6}) = - \frac{12}{( x - 6 ) ^{2}}

= 5 (\frac{x + 6}{x - 6})^{4} (- \frac{12}{( x - 6 ) ^{2}})

Vereinfache

5 (\frac{x + 6}{x - 6})^{4} (- \frac{12}{( x - 6 ) ^{2}}) : - \frac{60 ( x + 6 ) ^{4}}{( x - 6 ) ^{6}}

= - \frac{60 ( x + 6 ) ^{4}}{( x - 6 ) ^{6}}

Graph

Beliebte Beispiele

derivative of e^{-x/3}

\frac{d}{d x} (e^{- \frac{x}{3}})

integral of (1-x^2)^2x^2

\int (1 - x^{2})^{2} x^{2} d x

fläche y=3x^4-3x^2,y=8x^2

a re a y = 3 x^{4} - 3 x^{2}, y = 8 x^{2}

derivative y=(2x-3)^4(x^2+x+1)^5

d er i v a t i v e y = (2 x - 3)^{4} (x^{2} + x + 1)^{5}

derivative of a^{6x^2}

\frac{d}{d x} (a^{6 x^{2}})