Question Number 11567 by Nayon last updated on 28/Mar/17 $${why}\:\:\:\:\:\:{li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\:\frac{{f}\left({x}\right)}{{g}\left({x}\right)}={li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{f}'\left({x}\right)}{{g}'\left({x}\right)} \\ $$ Answered by mrW1 last updated on 28/Mar/17 $${l}'{hopital}'{s}\:{rule} \\ $$ Terms…
Question Number 11565 by Nayon last updated on 28/Mar/17 $${if}\:\frac{{dy}}{{dx}}={p}\:\:,{then}\:{why}\:{dy}={pdx}? \\ $$ Answered by mrW1 last updated on 28/Mar/17 $${if}\:\frac{{dy}}{{dx}}={p}\Rightarrow{y}={px} \\ $$$$\Rightarrow{dy}={pdx} \\ $$ Terms…
Question Number 11563 by Nayon last updated on 28/Mar/17 $${if}\:\:{f}\left({x}\right)={g}\left({y}\right) \\ $$$${then}\:{why}\:\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)=\frac{{d}}{{dy}}\left({g}\left({y}\right)\right)? \\ $$ Commented by mrW1 last updated on 28/Mar/17 $${this}\:{is}\:{not}\:{always}\:{correct}.\:{but} \\ $$$$\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)=\frac{{d}}{{dy}}\left({g}\left({y}\right)\right)×\frac{{dy}}{{dx}} \\…
Question Number 11552 by Nayon last updated on 28/Mar/17 $${find}\:\frac{{d}}{{dx}}\left({y}\right)\:{where}\:\:{y}=\overset{\sqrt{{x}}} {\:}\sqrt{\sqrt{{x}}} \\ $$$$ \\ $$ Answered by ajfour last updated on 28/Mar/17 $${y}\:=\:\left(\sqrt{{x}}\right)^{\frac{\mathrm{1}}{\:\sqrt{{x}}}} \\ $$$$\mathrm{ln}\:{y}\:=\frac{\mathrm{ln}\:\sqrt{{x}}}{\:\sqrt{{x}}}…
Question Number 11547 by Nayon last updated on 28/Mar/17 $$\:\:\:\:\:\:\:\:\:\:\frac{{d}}{{dx}}\left({x}^{{x}} \right)=?\left[{please}\:{give}\:{the}\:{answer}\:{with}\:{proof}\right] \\ $$ Answered by sma3l2996 last updated on 28/Mar/17 $${x}^{{x}} ={e}^{{xln}\left({x}\right)} \\ $$$${so}\:\:\frac{{d}\left({x}^{{x}} \right)}{{dx}}=\frac{{d}\left({e}^{{xln}\left({x}\right)}…
Question Number 11548 by Nayon last updated on 28/Mar/17 $$ \\ $$$${find}\:\frac{{d}}{{dx}}\left(\mathrm{2}^{{x}} \right) \\ $$ Answered by sma3l2996 last updated on 28/Mar/17 $$=\frac{{d}\left({e}^{{xln}\left(\mathrm{2}\right)} \right)}{{dx}}={ln}\left(\mathrm{2}\right){e}^{{xln}\left(\mathrm{2}\right)} ={ln}\left(\mathrm{2}\right)\mathrm{2}^{{x}}…
Question Number 11545 by Nayon last updated on 28/Mar/17 $${find}\frac{{dy}}{{dx}}\:{if}\:{x}^{{x}} {y}^{{y}} =\mathrm{1} \\ $$ Answered by Joel576 last updated on 28/Mar/17 $${y}^{{y}} \:=\:{x}^{−{x}} \\ $$$${y}\:\mathrm{ln}\:{y}\:=\:−{x}\:\mathrm{ln}\:{x}…
Question Number 11546 by Nayon last updated on 28/Mar/17 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:{f}\left({x}\right)=^{{x}} \sqrt{{x}}\:{find}\:\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{and}\:{for}\:{what}\:{x}\:,{we}\:{will}\:{get}\:{the}\: \\ $$$$\:{maximum}\:{of}\:{the}\:{function}..? \\ $$$$…
Question Number 142531 by mnjuly1970 last updated on 01/Jun/21 $$\: \\ $$$$\:\:{if}\:\:\:\:\boldsymbol{\phi}\:\left({q}\right):=\:\int_{\mathrm{1}} ^{\:\infty} \frac{\mathrm{1}}{\:\sqrt{{x}}\:\left({q}+{x}\right)^{{x}} }{dx} \\ $$$$\:\:\:\:{then}\:::\:\:{lim}\:_{{q}\rightarrow\mathrm{1}} \boldsymbol{\phi}\left({q}\right):=? \\ $$$$\:\:\:\:\:\: \\ $$ Terms of Service…
Question Number 142502 by nkuly last updated on 01/Jun/21 $$\frac{{dy}}{{dx}}\: \\ $$$${y}=\:\mathrm{3}{a}^{{x}} −\mathrm{cot}\:\mathrm{2}{x} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com