Category: Differentiation

Question Number 70705 by sadimuhmud 136 last updated on 07/Oct/19 $$\frac{\mathrm{d}}{\mathrm{dx}}\left({\log }_{10}\mathrm{x}\right)=?$$ Answered by $@ty@m123lastupdatedon07/Oct/19$$\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{\mathrm{log}_{{e}} \:{x}.}{\mathrm{log}_{{e}} \:\mathrm{10}}\right)=\frac{\mathrm{1}}{\mathrm{ln}\:\mathrm{10}}.\frac{{d}}{{dx}}\left(\mathrm{ln}\:{x}\right) \…

Question Number 70601 by oyemi kemewari last updated on 06/Oct/19 $$\mathrm{prove}\mathrm{thst}\mathrm{I}={\int }_0^{\mathrm{\infty }}\mathrm{f}(\mathrm{x}+\frac{1}{\times })\frac{\mathrm{lnx}}{\mathrm{x}}\mathrm{dx}=0$$ Answered by mind is power last updated on 06/Oct/19 $${let}\:{x}=\frac{\mathrm{1}}{{y}}\Rightarrow{I}=\int_{\infty}…

Question Number 70582 by Raphael last updated on 05/Oct/19 $$\mathrm{Given}\mathrm{that}\mathrm{y}=\frac{4}{\sqrt{({\mathrm{x}}^3+1)}}\mathrm{show}\mathrm{that}2({\mathrm{x}}^3+1)\frac{\mathrm{dy}}{\mathrm{dx}}=-{3\mathrm{x}}^2\mathrm{y}.$$ Commented by kaivan.ahmadi last updated on 05/Oct/19 $$\mathrm{2}\left({x}^{\mathrm{3}} +\mathrm{1}\right)×\frac{−\frac{\mathrm{4}×\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}\sqrt{{x}^{\mathrm{3}}…

Question Number 4993 by love math last updated on 29/Mar/16 $$f\left(x\right)=\frac{xlnx}{1+e^x}$$$$$$$$f{}^{\prime }\left(x\right)-?$$ Answered by FilupSmith last updated on 30/Mar/16…

Question Number 136006 by liberty last updated on 17/Mar/21 $$$$What are the dimensions of the rectangle of maximum area that can be inscribed…