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
Question Number 76952 by ~blr237~ last updated on 01/Jan/20 $$\mathrm{show}\:\mathrm{that}\: \\ $$$$\sqrt{\mathrm{1}+\:\mathrm{2017}×\mathrm{2018}×\mathrm{2019}×\mathrm{2020}\:}\:\in\:\mathbb{N} \\ $$ Answered by MJS last updated on 01/Jan/20 $$\mathrm{1}+{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)= \\ $$$$={x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{3}}…
Question Number 76941 by ~blr237~ last updated on 01/Jan/20 $$\mathrm{We}\:\mathrm{usually}\:\mathrm{have}\:\mathrm{to}\:\mathrm{write}\:\mathrm{the}\:\mathrm{date}\:\mathrm{in}\:\mathrm{this}\:\mathrm{form}\:\mathrm{01}/\mathrm{01}/\mathrm{2020} \\ $$$$\mathrm{to}\:\mathrm{mean}\:\mathrm{the}\:\mathrm{1}^{\mathrm{st}} \:\mathrm{january}\:\mathrm{2020}\: \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{first}\:\mathrm{date}\:\mathrm{that}\:\mathrm{is}\:\mathrm{written}\:\mathrm{in}\:\mathrm{this}\:\mathrm{form}\:\mathrm{with}\:\mathrm{eight}\:\mathrm{different}\:\mathrm{figures}\:? \\ $$$$\mathrm{an}\:\mathrm{example}\::\:\mathrm{25}/\mathrm{09}/\mathrm{1873}\:\: \\ $$$$“\mathrm{i}\:\mathrm{wish}\:\mathrm{you}\:\mathrm{a}\:\mathrm{sweet}\:\mathrm{and}\:\mathrm{happy}\:\mathrm{new}\:\mathrm{year}\:\mathrm{to}\:\mathrm{all}\:\mathrm{of}\:\mathrm{you}'' \\ $$ Commented by mr W…