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Category: Differentiation

Question-57084

Question Number 57084 by frimpshaddie last updated on 30/Mar/19 Commented by Kunal12588 last updated on 30/Mar/19 $$\left({d}\right)\:{when}\:{the}\:{velocity}\:{of}\:{particle}\:{becomes}\:\mathrm{0} \\ $$$${then}\:{the}\:{particle}\:{is}\:{said}\:{to}\:{be}\:{in}\:{rest} \\ $$$$\left({horizontal}\:{motion}\:{only}\right) \\ $$$$\therefore{v}=\mathrm{0} \\ $$$$\Rightarrow\mathrm{3}{t}^{\mathrm{2}}…

nice-calculus-prove-that-0-1-ln-1-x-2-x-dx-pi-2-12-m-n-1970-

Question Number 122525 by mnjuly1970 last updated on 17/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:{prove}\:{that}\:\:\::::::\gg\:\:\:\Psi=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{2}−{x}}{dx}=−\frac{\pi^{\mathrm{2}} }{\mathrm{12}}\:\checkmark \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:…\:{m}.{n}.\mathrm{1970}… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by Dwaipayan Shikari…

find-dy-dx-y-2x-x-

Question Number 188037 by Michaelfaraday last updated on 25/Feb/23 $${find}\:\frac{{dy}}{{dx}} \\ $$$${y}=\mathrm{2}{x}^{\sqrt{{x}}} \\ $$ Answered by horsebrand11 last updated on 25/Feb/23 $$\:\mathrm{ln}\:{y}=\sqrt{{x}}\:\mathrm{ln}\:\left(\mathrm{2}{x}\right) \\ $$$$\:\frac{\mathrm{1}}{{y}}.{y}'=\frac{\mathrm{ln}\:\left(\mathrm{2}{x}\right)}{\mathrm{2}\sqrt{{x}}}+\frac{\mathrm{2}\sqrt{{x}}}{\mathrm{2}{x}} \\…

Question-188017

Question Number 188017 by Rupesh123 last updated on 24/Feb/23 Answered by aleks041103 last updated on 24/Feb/23 $${f}\left({x},{y}\right)={ln}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)=\mathrm{2}{ln}\left({r}\right) \\ $$$${r}=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } \\ $$$$\Rightarrow{f}\left({x},{y}\right)={f}\left({r}\right)…

If-f-x-a-a-x-3-dt-1-sin-2-t-dt-1-sin-2-t-then-f-x-

Question Number 122434 by benjo_mathlover last updated on 17/Nov/20 $$\:{If}\:{f}\left({x}\right)\:=\:\int_{{a}} ^{\:\left(\underset{{a}} {\overset{{x}^{\mathrm{3}} } {\int}}\:\frac{{dt}}{\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} {t}}\:\right)} \left(\frac{{dt}}{\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} {t}}\right) \\ $$$${then}\:{f}\:'\left({x}\right)\:? \\ $$ Answered by liberty last…