If y=x.log(x/a+bx).prove that d^2y/dx^2=1/x(a/a+bx)^2

Dear student

Differentiating both sides with respect to x, we have

Now, from (1) we have

Differentiating both sides with respect to x, we have

$\Rightarrow \frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}=\frac{1}{\mathrm{x}}{\left(\frac{\mathrm{a}}{\mathrm{a}+\mathrm{bx}}\right)}^2$
Regards