02-20-2014, 10:56 PM

The following comparison fails (which is true when you do it by hand):

$$\frac{\partial \left( \frac{x^n}{n^3\cdot\left(1+x^n\right)}\right)}{\partial x} =\frac{x^{n-1}}{n^2\cdot(x^n)^2+2\cdot n^2\cdot x^n+n^2}== \frac{x^{n-1}}{n^2\cdot\left(1+x^n\right)^2}$$

(The term in the middle is what the differential is solved to by the Prime. It doesn't matter whether it is compared directly to the differential or to the solution).

It also doesn't matter whether you make the following assumptions about x and n:

n Integer and >0

x >0

$$\frac{\partial \left( \frac{x^n}{n^3\cdot\left(1+x^n\right)}\right)}{\partial x} =\frac{x^{n-1}}{n^2\cdot(x^n)^2+2\cdot n^2\cdot x^n+n^2}== \frac{x^{n-1}}{n^2\cdot\left(1+x^n\right)^2}$$

(The term in the middle is what the differential is solved to by the Prime. It doesn't matter whether it is compared directly to the differential or to the solution).

It also doesn't matter whether you make the following assumptions about x and n:

n Integer and >0

x >0