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Category: Differentiation

Question-68350

Question Number 68350 by mhmd last updated on 09/Sep/19 Commented by MJS last updated on 09/Sep/19 $$\left({x}−\mathrm{2cos}\:\frac{\mathrm{2}\pi}{\mathrm{7}}\right)\left({x}−\mathrm{2cos}\:\frac{\mathrm{4}\pi}{\mathrm{7}}\right)\left({x}−\mathrm{cos}\:\frac{\mathrm{6}\pi}{\mathrm{7}}\right)=\mathrm{0} \\ $$$$\mathrm{approximating}\:\mathrm{leads}\:\mathrm{to} \\ $$$${x}^{\mathrm{3}} +{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{we}\:\mathrm{have}\:\mathrm{to}\:\mathrm{show}\:\mathrm{that}…

Differentiate-y-ln-tan-1-3x-2-

Question Number 68331 by Peculiar last updated on 08/Sep/19 $${Differentiate}\:{y}={ln}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{3}{x}^{\mathrm{2}} \underset{} {\right)} \\ $$ Answered by MJS last updated on 08/Sep/19 $${y}={h}\left({g}\left({f}\left({x}\right)\right)\right) \\ $$$${y}'={h}'\left({g}\left({f}\left({x}\right)\right)\right)×{g}'\left({f}\left({x}\right)\right)×{f}'\left({x}\right)…

Question-133859

Question Number 133859 by mnjuly1970 last updated on 24/Feb/21 Answered by Ñï= last updated on 24/Feb/21 $$\underset{{n}=−\infty} {\overset{+\infty} {\sum}}\frac{\mathrm{1}}{\left({x}+{n}\pi\right)^{\mathrm{2}} } \\ $$$$=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left[\frac{\mathrm{1}}{\left({x}+{n}\pi\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({x}−{n}\pi\right)^{\mathrm{2}}…

Prove-that-if-Li-2-x-n-1-x-n-n-2-then-x-Li-2-x-Li-2-1-x-pi-2-6-ln-x-ln-1-x-x-0-1-Li-2-x-Li-2-1-x-pi-2-6-ln-x-2-Find-A-n-1-n-n-2-an

Question Number 68270 by ~ À ® @ 237 ~ last updated on 08/Sep/19 $$\:{Prove}\:{that}\:\:{if}\:\:{Li}_{\mathrm{2}} \left({x}\right)=\underset{{n}=\mathrm{1}} {\sum}\:\frac{{x}^{{n}} }{{n}^{\mathrm{2}} }\:\:\:{then} \\ $$$$\forall\:{x}\:\:{Li}_{\mathrm{2}} \left({x}\right)+{Li}_{\mathrm{2}} \left(\mathrm{1}−{x}\right)\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}}\:−{ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right)\:\: \\…

n-3-1-n-ln-n-2-is-the-function-converg-or-diverg-pleas-help-me-

Question Number 68188 by mhmd last updated on 06/Sep/19 $$\sum_{{n}=\mathrm{3}} ^{\propto} \:\mathrm{1}/{n}\left({ln}\:{n}\right)^{\mathrm{2}} \:\:\:{is}\:{the}\:{function}\:{converg}\:{or}\:{diverg}\:?\:{pleas}\:{help}\:{me} \\ $$ Commented by Abdo msup. last updated on 07/Sep/19 $${let}\:\varphi\left({x}\right)\:=\frac{\mathrm{1}}{{x}\left({lnx}\right)^{\mathrm{2}} }\:\:{with}\:\:{x}\geqslant\mathrm{3}\:\:{we}\:{have}…

Suppose-function-f-R-R-with-f-2x-3-4x-2-2x-5-and-f-denote-is-derivatif-of-f-function-What-the-value-of-f-2x-3-

Question Number 133616 by benjo_mathlover last updated on 23/Feb/21 $$\mathrm{Suppose}\:\mathrm{function}\:\mathrm{f}:\mathrm{R}\rightarrow\mathrm{R}\:\mathrm{with} \\ $$$$\mathrm{f}\left(\mathrm{2x}−\mathrm{3}\right)\:=\:\mathrm{4x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{5}\:\mathrm{and}\:\mathrm{f}\:'\:\mathrm{denote} \\ $$$$\mathrm{is}\:\mathrm{derivatif}\:\mathrm{of}\:\mathrm{f}\:\mathrm{function}. \\ $$$$\mathrm{What}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\:'\left(\mathrm{2x}−\mathrm{3}\right) \\ $$ Commented by mr W last updated…