Consider the following statements

Statement 1 : If $$y=\log _{10} x+\log _e x$$, then $$\frac{d y}{d x}=\frac{\log _{10} e}{x}+\frac{1}{x}$$

Statement 2 : If $$\frac{d}{d x}\left(\log _{10} x\right)=\frac{\log x}{\log 10}$$ and $$\frac{d}{d x}\left(\log _e x\right)=\frac{\log x}{\log e}$$

If the parametric equation of curve is given by $$x=\cos \theta+\log \tan \frac{\theta}{2}$$ and $$y=\sin \theta$$, then the points for which $$\frac{d y}{d x}=0$$ are given by

If $$y=(x-1)^2(x-2)^3(x-3)^5$$, then $$\frac{d y}{d x}$$ at $$x=4$$ is equal to

If $$2^x+2^y=2^{x+y}$$, then $$\frac{d y}{d x}$$ is