Question Number 2071 by Rasheed Soomro last updated on 01/Nov/15 $$\left\{\:\left[{f}\left({x}\right)\right]^{−\mathrm{1}} \right\}'\:=\left[\:{f}\:'\left({x}\right)\:\right]^{−\mathrm{1}} \\ $$$${f}\left({x}\right)=? \\ $$ Commented by Yozzi last updated on 01/Nov/15 $$\frac{{d}}{{dx}}\left(\frac{\mathrm{1}}{{f}\left({x}\right)}\right)=\frac{\mathrm{1}}{{f}^{'} \left({x}\right)}…
Question Number 2035 by Rasheed Soomro last updated on 31/Oct/15 $${f}\left(\:{f}\:'\left({x}\right)\:\right)={f}\:'\left(\:{f}\left({x}\right)\:\right) \\ $$$${f}\left({x}\right)=? \\ $$ Commented by Yozzi last updated on 31/Oct/15 $${Try}\:{f}\left({x}\right)={e}^{{x}} .\:{f}^{'} \left({x}\right)={e}^{{x}}…
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Question Number 2007 by Rasheed Soomro last updated on 29/Oct/15 $${Determine} \\ $$$$\left({i}\right)\:\:\frac{{d}}{{dx}}\left({x}^{\frac{\mathrm{1}}{{x}}} \right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({ii}\right)\:\int\:{x}^{\frac{\mathrm{1}}{{x}}} {dx} \\ $$ Answered by Yozzi last updated on 29/Oct/15 $${Let}\:{y}={x}^{\mathrm{1}/{x}}…
Question Number 2006 by Rasheed Soomro last updated on 29/Oct/15 $${Determine} \\ $$$$\left({i}\right)\:\:\frac{{d}}{{dx}}\left({x}^{{x}} \right)\:\:\:\:\:\:\:\:\:\:\:\left({ii}\right)\:\:\int{x}^{{x}} \:{dx} \\ $$ Answered by 123456 last updated on 29/Oct/15 $${y}={x}^{{x}}…
Question Number 2005 by Rasheed Soomro last updated on 29/Oct/15 $${If}\:{f}\left({x}\right)\:{and}\:{g}\left({x}\right)\:{have}\:{no}\:{constant}\:{term}\:{then} \\ $$$${f}\:'\left({x}\right)={g}'\left({x}\right)\overset{?} {\:\Rightarrow\:}{f}\left({x}\right)={g}\left({x}\right)? \\ $$ Commented by prakash jain last updated on 30/Oct/15 $$\mathrm{If}\:{f}\left({x}\right)\neq{g}\left({x}\right)…
Question Number 67465 by ~ À ® @ 237 ~ last updated on 27/Aug/19 $$ \\ $$$$ \\ $$$$\:\:{let}\:{consider}\:{a}\:{function}\:{g}\:{defined}\:{by}\:\:\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dx}}{\:\sqrt{\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+{ax}\right)}}\:\: \\ $$$${Give}\:{the}\:{defined}\:{Domain}\:{of}\:{g}\:\:{and}\:{simplify}\:{g}. \\ $$…
Question Number 67398 by mhmd last updated on 26/Aug/19 $${solve}\:{the}\:{defrintion}\:{eguation}\:\left({xp}^{\mathrm{2}} −{p}+\mathrm{2}{x}\right)=\mathrm{0} \\ $$$${when}\:{p}={dy}/{dx} \\ $$ Commented by mathmax by abdo last updated on 26/Aug/19 $${xy}^{''}…
Question Number 67393 by Prof 40 last updated on 26/Aug/19 $${let}\:{y}=\left({x}−\mathrm{3}\right)\phi\left(\mathrm{2}{x}+\mathrm{1}\right) \\ $$$${find}\:{dy}/{dx}\:{when}\:{x}=\mathrm{2} \\ $$ Commented by mathmax by abdo last updated on 27/Aug/19 $${if}\:{we}\:{suppose}\:{that}\:\varphi\:{is}\:{a}\:{function}\:\:{we}\:{get}…
Question Number 67382 by Mikael last updated on 26/Aug/19 $${calculate}\:{if}\:{there}\:{are}\:{maxims}\:{and}\:{minimus}\:{of} \\ $$$${the}\:{following}\:{function}: \\ $$$${y}=\begin{cases}{{x}^{\mathrm{2}} +\mathrm{1}\:{if}\:{x}\lneq\mathrm{1}}\\{−{x}+\mathrm{4}\:{if}\:{x}\geqslant\mathrm{1}}\end{cases} \\ $$ Commented by mr W last updated on 26/Aug/19…