Differentiate with respect to x loge^x /x^2?

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    log(eˣ)

   ———–            ← log(eˣ) is written as a common logarithm.

       x²                     So, with that in mind, we need to convert

                               to natural logarithms in order to differentiate.

   ln(eˣ) / ln10            ← Converted to natural logarithms

= —————–

          x²

     ln(eˣ)

= ———–

    x² ln10

        x

= ————

     x²  ln10

        1

= ———–            ← Now, differentiate

      x  ln10

   d(1/ln10) x⁻¹                                  −1

   —————  =  (1/ln10)(-1/x²)  =  ————            ← ANSWER

         dx                                         x²  ln10

Have a good one!

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Xloge^x=x*x=x^2

so F(X)=(Xloge^X)/X^2=X^2/X^2=1

F'(X)=0

Would be more than happy to answer question if I could be sure as to how it is meant to be read.

Brackets MUST be used.

f(x) = ln(e^x) /x^2 = 1/x

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