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Beliebt Rechnen >

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

Lösung

\frac{d}{d x} ((\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

fläche x=-5,x=3,y=2x^2+12,y=0

a re a x = - 5, x = 3, y = 2 x^{2} + 12, y = 0

integral of 1/((x-2)(x-5))

\int \frac{1}{( x - 2 ) ( x - 5 )} d x

(\partial)/(\partial x)(3x^2+2xy-7y^2)

\frac{\partial}{\partial x} (3 x^{2} + 2 x y - 7 y^{2})

f^{^{'}} (x) = x

derivative of sqrt(1+x^4)

\frac{d}{d x} (1 + x^{4})