Category: Differentiation

Question Number 30187 by abdo imad last updated on 17/Feb/18 $$solve{xy}^{{}^{\prime }}-2y=x^4.$$ Answered by ajfour last updated on 18/Feb/18 $$\frac{dy}{dx}-\left(\frac{2}{x}\right)y=x^3$$$${e}^{−\int\frac{\mathrm{2}}{{x}}{dx}}…

Question Number 161209 by CM last updated on 14/Dec/21 $$Differentiatey=e^{-x^2}$$ Commented by cortano last updated on 14/Dec/21 $$\iff \ln y=-x^2$$$$\iff \frac{y^{\prime }}{y}=-2x$$$$\Leftrightarrow\:{y}'\:=\:−\mathrm{2}{x}\:{e}^{−{x}^{\mathrm{2}}…

Question Number 95644 by Ar Brandon last updated on 26/May/20 $$\mathrm{If}\mathrm{f}\mathrm{is}\mathrm{derivable}\mathrm{at}{\mathrm{x}}_0,\mathrm{show}\mathrm{that}\underset{\mathrm{x}\to {\mathrm{x}}_0}{\lim f}\left(\mathrm{x}\right)=\mathrm{f}\left({\mathrm{x}}_0\right)$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 95638 by Ar Brandon last updated on 26/May/20 $$\mathrm{a}\mathrm{\setminus }\mathrm{Show}\mathrm{that}\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}}\mathrm{is}\mathrm{derivable}\mathrm{at}\mathrm{all}\mathrm{points}{\mathrm{x}}_0>0$$$$\mathrm{and}\mathrm{that}{\mathrm{f}}^{\prime }\left({\mathrm{x}}_0\right)=\frac{1}{{2\mathrm{x}}_0}$$$$\mathrm{b}\mathrm{\setminus }\mathrm{Show}\mathrm{that}\mathrm{the}\mathrm{function}\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}}(\mathrm{continuous}\mathrm{at}{\mathrm{x}}_0=0)$$$$\mathrm{is}\mathrm{not}\mathrm{derivable}\mathrm{at}{\mathrm{x}}_0=0$$ Answered…

Question Number 95635 by Ar Brandon last updated on 26/May/20 $$\mathrm{Show}\mathrm{that}\mathrm{if}\mathrm{a}\mathrm{function}\mathrm{is}\mathrm{even}\mathrm{and}\mathrm{derivable}\mathrm{then}$$$${\mathrm{f}}^{\prime }\left(\mathrm{x}\right)\mathrm{is}\mathrm{an}\mathrm{odd}\mathrm{function}.$$ Answered by mr W last updated on 26/May/20 $${f}\left({x}\right)\:{is}\:{even}:\:{f}\left(−{x}\right)={f}\left({x}\right) \…