Question

What is the derivative of
`f(x)=(In(x))/(x)~?`

Answer 1

Answer and Step-by-step explanation:

`Greetings!`

`Let's~answer~your~question!`

→
`By~quotient~rule,`

`y'=((1)/(x)*x~-~In~x*1 )/(x^2) =(1-In~x)/(x^2)`

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`This~ problem ~can ~also ~be ~solved ~by~ the ~Product~ Rule:`

`y'=f'(x)~g(x)+f(x)~g(x)`

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`The~ original~ function ~can~ also~be~ rewritten~ using ~negative~ exponents:`

`f(x)=(In(x))/(x)=In(x)*x^-^1`

`f'(x)=(1)/(x) *x^-^1+ln(x)*-1x^-^2`

`f'(x)=(1)/(x)*(1)/(x)+In(x)*-(1)/(x^2)`

`f'(x)=(1)/(x^2)-(In(x))/(x^2)`

`f'(x)=(1-In(x))/(x^2)`