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Differentiating a Logarithmic Function In Exercise, find the derivative of the function.

y =In x(x - 1)/x - 2

User Abhic
by
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1 Answer

2 votes

Answer:


(d)/(dx) ln((x(x-1))/(x-2)) = (x-2)/(x(x-1)) (x^2 -4x +2)/((x-2)^2) = (x^2 -4x +2)/(x(x-1)(x-2))

Explanation:

For this case we want to find the derivate of this function:


y = ln((x(x-1))/(x-2))

And in order to find the derivate we need to apply the chain rule given by:


(df(u))/(dx) =(df)/(du) (du)/(dx)

And on this case
f = ln(u), u = (x(x-1))/(x-2)

And we can find the partial derivates like this:


(d)/(du) (ln(u))= (1)/(u)


(d)/(dx)((x(x-1))/(x-2))= ((2x-1)(x-2) -x(x-1))/((x-2)^2)= (x^2 -4x +2)/((x-2)^2)

And if we replace we got:


(d)/(dx) ln((x(x-1))/(x-2)) = (1)/(u) (x^2 -4x +2)/((x-2)^2)

And if we replace
u = (x(x-1))/(x-2) we got:


(d)/(dx) ln((x(x-1))/(x-2)) = (x-2)/(x(x-1)) (x^2 -4x +2)/((x-2)^2) = (x^2 -4x +2)/(x(x-1)(x-2))

And that would be our final answer on this case

User Bubblez
by
5.7k points
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