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Beliebt Rechnen >

derivative of ((x-5/(x+5))^4)

Lösung

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

Lösung

\frac{40 ( x - 5 ) ^{3}}{( x + 5 ) ^{5}}

Schritte zur Lösung

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

Wende die Kettenregel an:

4 (\frac{x - 5}{x + 5})^{3} \frac{d}{d x} (\frac{x - 5}{x + 5})

= 4 (\frac{x - 5}{x + 5})^{3} \frac{d}{d x} (\frac{x - 5}{x + 5})

\frac{d}{d x} (\frac{x - 5}{x + 5}) = \frac{10}{( x + 5 ) ^{2}}

= 4 (\frac{x - 5}{x + 5})^{3} \frac{10}{( x + 5 ) ^{2}}

Vereinfache

4 (\frac{x - 5}{x + 5})^{3} \frac{10}{( x + 5 ) ^{2}} : \frac{40 ( x - 5 ) ^{3}}{( x + 5 ) ^{5}}

= \frac{40 ( x - 5 ) ^{3}}{( x + 5 ) ^{5}}

Graph

Beliebte Beispiele

integral of (x^3)/(x^2-x-2)

\int \frac{x ^{3}}{x ^{2} - x - 2} d x

derivative y=sqrt(x)+x^pi

d er i v a t i v e y = x + x^{π}

tangent f(x)= 1/(4+3x),\at x=2

t an g e n t f (x) = \frac{1}{4 + 3 x}, at x = 2

y=-x^{-1}+3/5 x+1/2

y = - x^{- 1} + \frac{3}{5} x + \frac{1}{2}

integral of (t^2+2t+1)^4(t+1)

\int (t^{2} + 2 t + 1)^{4} (t + 1) d t