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Beliebt Rechnen >

derivative of ((x-7/(x-9))^4)

Lösung

\frac{d}{d x} ((\frac{x - 7}{x - 9})^{4})

Lösung

- \frac{8 ( x - 7 ) ^{3}}{( x - 9 ) ^{5}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x - 7}{x - 9})^{4})

Wende die Kettenregel an:

4 (\frac{x - 7}{x - 9})^{3} \frac{d}{d x} (\frac{x - 7}{x - 9})

= 4 (\frac{x - 7}{x - 9})^{3} \frac{d}{d x} (\frac{x - 7}{x - 9})

\frac{d}{d x} (\frac{x - 7}{x - 9}) = - \frac{2}{( x - 9 ) ^{2}}

= 4 (\frac{x - 7}{x - 9})^{3} (- \frac{2}{( x - 9 ) ^{2}})

Vereinfache

4 (\frac{x - 7}{x - 9})^{3} (- \frac{2}{( x - 9 ) ^{2}}) : - \frac{8 ( x - 7 ) ^{3}}{( x - 9 ) ^{5}}

= - \frac{8 ( x - 7 ) ^{3}}{( x - 9 ) ^{5}}

Graph

Beliebte Beispiele

integral of (ln(20x))/x

\int \frac{ln ( 20 x )}{x} d x

\frac{d}{d y} (- e^{y})

(d^2y)/(dx^2)+16y=0

\frac{d ^{2} y}{d x ^{2}} + 16 y = 0

derivative f(x)=-x^3+2x-e^{-x}-3

d er i v a t i v e f (x) = - x^{3} + 2 x - e^{- x} - 3

inverselaplace 3/(\frac{s+2){s}}

in v erse l a pl a ce \frac{3}{\frac{s + 2}{s}}