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Category: Differentiation

Question-208855

Question Number 208855 by efronzo1 last updated on 25/Jun/24 Answered by mr W last updated on 25/Jun/24 $${let}\:{t}=\mathrm{1}+\mid{x}\mid\geqslant\mathrm{1} \\ $$$$\frac{\mathrm{2024}^{−{t}} −\lambda}{\mathrm{2024}^{−{t}} −\lambda^{−\mathrm{1}} }=\lambda\:\mathrm{2024}^{{t}} \\ $$$$\mathrm{2024}^{−{t}}…

If-y-1-x-1-x-2-1-x-4-1-x-2n-then-find-dy-dx-at-x-0-

Question Number 207109 by MATHEMATICSAM last updated on 06/May/24 $$\mathrm{If}\:{y}\:=\:\left(\mathrm{1}\:+\:{x}\right)\left(\mathrm{1}\:+\:{x}^{\mathrm{2}} \right)\left(\mathrm{1}\:+\:{x}^{\mathrm{4}} \right)\:….\:\left(\mathrm{1}\:+\:{x}^{\mathrm{2}{n}} \right) \\ $$$$\mathrm{then}\:\mathrm{find}\:\frac{{dy}}{{dx}}\:\mathrm{at}\:{x}\:=\:\mathrm{0}. \\ $$ Answered by Berbere last updated on 06/May/24 $${y}\left({x}\right)=\left(\mathrm{1}+{x}\right)\underset{{k}=\mathrm{1}}…

f-x-tan-2-x-tan-x-tan-x-tan-x-tan-x-1-5-1-4-1-3-f-pi-4-

Question Number 206882 by efronzo1 last updated on 29/Apr/24 $$\:\:{f}\left({x}\right)=\mathrm{tan}\:^{\mathrm{2}} {x}\:\sqrt{\mathrm{tan}\:{x}\sqrt[{\mathrm{3}}]{\mathrm{tan}\:{x}\sqrt[{\mathrm{4}}]{\mathrm{tan}\:{x}\sqrt[{\mathrm{5}}]{\mathrm{tan}\:{x}\sqrt{…}}}}} \\ $$$$\:{f}\:'\left(\frac{\pi}{\mathrm{4}}\right)=? \\ $$ Answered by MM42 last updated on 29/Apr/24 $${f}\left({x}\right)={tan}^{\mathrm{2}} {x}×{tan}^{\frac{\mathrm{1}}{\mathrm{2}}} {x}×{tan}^{\frac{\mathrm{1}}{\mathrm{6}}}…

0-1-ln-1-x-ln-1-x-x-dx-n-1-n-find-n-1-n-n-

Question Number 206340 by mnjuly1970 last updated on 12/Apr/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\:{ln}\left(\mathrm{1}−{x}\:\right){ln}\left(\mathrm{1}+{x}\:\right)}{{x}}{dx}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\Omega_{{n}} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:{find}\::\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\:{n}\:\Omega_{{n}} \:=\:? \\ $$…