Find the derivative of a function ln ⁡ x x .

Question

Find the derivative of a function             ln      ⁡      x        x  .

Aleah Rowe · Accepted Answer

The quotient rule states that:  (      f    g    )  =            f              ′            g      −      f      g              ′                    g              2            where the apostrophe   (      ′    ) means &quot;the derivative of&quot;.In this example, we let   f  =  ln  ⁡  x and   g  =  xThis allows us to rewrite the function as:            (      (              d                  d          x                    ln      ⁡      x      )      x      −      ln      ⁡      x      (      (              d                  d          x                    )      x      )              x              2            Other calculus rules tell us that the derivative of   ln  ⁡  x is always       1    x  . As a result, the first half of our numerator becomes   x  (      1    x    ), Which neatly simplifies to   1. This gives:            1      −      ln      ⁡      x      (      (              d                  d          x                    )      x      )              x              2            Now we can use the power rule, which states that   (      d          d      x        )      x          n        =  n      x          n      −      1      . Since we know that nn in this case is   1 (because   x  has no exponent), this becomes   1  ×      x          1      −      1      , which yields a value of   1. This gives us our final answer:            1      −      ln      ⁡      x              x              2

Find the derivative of a function lnx/x

Answered question

Answer & Explanation

New Questions in Calculus 1