$y=\ln{x}+x$ হলে, $x\frac{dy}{dx}-y=\ ?$

দৃশ্যকল্প-I: $y(x+1)(x+2)-x+4$

দৃশ্যকল্প-II: $\mathrm{g}(\mathrm{x})=3 \mathrm{x}^{3}-6 \mathrm{x}^{2}-5 \mathrm{x}+1$

Let $f\left( x \right) =\left\{ \begin{matrix} { x }^{ { 3 }/{ 5 } }\quad \quad \quad x\le 1 \\ -{ \left( x-2 \right) }^{ 3 }\quad x>1 \end{matrix} \right.$

then the number of critical points on the graph of the function is

If for all $x, y$ the function f is defined by; $f(x)+f(y)+f(x)\cdot f(y)=1$ and $f(x) > 0$.When $f(x)$ is differentiable $f'(x)=$,

x এর কোন মানের জন্য   $f{\left ( x \right )} = \frac{x}{\ln{x}}$ সর্বনিম্ন হবে-