Find h' (x) where f(x) is unspecified differentiable function and `h(x) = f(x)/ln x`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function `h(x) = f(x) / ln x` where f(x) is an unspecified differentiable function.

Using the quotient rule for ` h(x) = (f(x))/(g(x))` , `h'(x) = (f'(x)*g(x) - f(x)*g'(x))/(g(x))^2`

Substituting `g(x) = ln x`

`h'(x) = (f'(x)*ln x - f(x)/x)/(ln x)^2`

The required derivative `h'(x) = (f'(x)*ln x - f(x)/x)/(ln x)^2`

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