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Category: Differentiation

calculus-I-If-I-0-pi-x-1-sin-2-x-dx-a-2-a-where-s-n-1-1-n-s-

Question Number 200418 by mnjuly1970 last updated on 18/Nov/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{calculus}\:\:\left(\:\:\mathrm{I}\:\:\right)\:\: \\ $$$$\:\:\mathrm{I}{f}\:,\:\:\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\pi} \:\frac{\:{x}\:}{\mathrm{1}\:\:+\:\mathrm{sin}^{\mathrm{2}} \left({x}\right)}\:\mathrm{d}{x}\:=\:{a}\:\zeta\:\left(\:\mathrm{2}\:\right)\:\: \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:\:\:{a}\:=\:?\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:{where}\:\:,\:\:\:\zeta\:\left({s}\:\right)\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\:\mathrm{1}}{{n}^{\:{s}} } \\…

Question-200251

Question Number 200251 by Calculusboy last updated on 16/Nov/23 Answered by Mathspace last updated on 16/Nov/23 $${f}\left({x},{y}\right)={sin}\left({e}^{{xy}} +{e}^{{x}} \right)\:\Rightarrow \\ $$$$\frac{\partial}{\partial{x}}{f}\left({x},{y}\right)=\frac{\partial}{\partial{x}}\left({e}^{{xy}} +{e}^{{x}} \right){cos}\left({e}^{{xy}} +{e}^{{x}} \right)…

f-x-3x-5-2x-1-f-x-

Question Number 198953 by ArifinTanjung last updated on 26/Oct/23 $$\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{3x}−\mathrm{5}}{\mathrm{2x}+\mathrm{1}}\:\rightarrow\mathrm{f}^{'} \left(\mathrm{x}\right)=….? \\ $$ Answered by Rasheed.Sindhi last updated on 26/Oct/23 $$\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{3x}−\mathrm{5}}{\mathrm{2x}+\mathrm{1}}\:\rightarrow\mathrm{f}^{'} \left(\mathrm{x}\right)=….? \\ $$$$\left(\frac{{u}}{{v}}\right)^{'} =\frac{{v}\:{u}'−{u}\:{v}'}{{v}^{\mathrm{2}}…

Question-198988

Question Number 198988 by Safojon last updated on 26/Oct/23 Answered by witcher3 last updated on 26/Oct/23 $$\mathrm{f}\left(\mathrm{x}\right)−\mathrm{g}\left(\mathrm{x}\right)=\mathrm{x}\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{1010}} {\sum}}\left(\mathrm{x}^{\mathrm{2k}} \right)>\mathrm{0} \\ $$$$\mathrm{u}_{\mathrm{n}} =\mathrm{f}^{\left(\mathrm{n}\right)} \left(\frac{\mathrm{1}}{\mathrm{2023}}\right),\mathrm{v}_{\mathrm{n}} =\mathrm{g}^{\left(\mathrm{n}\right)}…

f-tan-x-2f-cot-x-4x-f-x-

Question Number 198562 by cortano12 last updated on 22/Oct/23 $$\:\:\:\mathrm{f}\left(\mathrm{tan}\:\mathrm{x}\right)+\:\mathrm{2f}\left(\mathrm{cot}\:\mathrm{x}\right)\:=\:\mathrm{4x}\: \\ $$$$\:\:\:\mathrm{f}\:'\left(\mathrm{x}\right)=\:? \\ $$ Answered by dimentri last updated on 22/Oct/23 $$\:{let}\:{x}=\frac{\pi}{\mathrm{2}}−{t}\: \\ $$$$\:{f}\left(\mathrm{cot}\:{t}\right)\:+\mathrm{2}\:{f}\left(\mathrm{tan}\:{t}\right)=\:\mathrm{2}\pi−\mathrm{4}{t} \\…