Find the derivative of f(x) = (x^2-3x+2)*ln x

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The function f(x) = (x^2 - 3x + 2)*ln x

f'(x) can be found using the product rule as

f'(x) = (x^2 - 3x + 2)'*ln x + (x^2 - 3x + 2)*(ln x)'

(2x - 3)*ln x + (x^2 - 3x + 2)*(1/x)

=> (2x - 3)*ln x + x - 3 +2/x

=> 2x*ln x - 3*ln x + x - 3 + 2/x

The derivative of the given function is 2x*ln x - 3*ln x + x - 3 + 2/x

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given f(x) = (x^2 - 3x + 2) * ln x

We will use the product rule to find the derivative.

Let f(x) = u*v such that:

u= x^2 -3x + 2  ==> u' = 2x-3

v = ln x ===>    v' = 1/x

==> f'(x) = u'*v + u*v'

==> f'(x) = ( 2x-3)*lnx + (x^2 - 3x + 2)*1/x

==> f'(x) = (2x-3)ln x + (x -3 + 2/x)

==> f'(x) = (2x-3)lnx + x + 2/x - 3

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