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Category: Differentiation

f-x-x-sinx-0-lt-x-lt-pi-2-find-f-x-

Question Number 69680 by 20190927 last updated on 26/Sep/19 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{sinx}} \:\:,\:\mathrm{0}<\mathrm{x}<\frac{\pi}{\mathrm{2}}\:\:\:\mathrm{find}\:\mathrm{f}'\left(\mathrm{x}\right) \\ $$ Answered by MJS last updated on 26/Sep/19 $$\frac{{d}}{{dx}}\left[{u}^{{v}} \right]={u}^{{v}} \left(\frac{{u}'{v}}{{u}}+{v}'\mathrm{ln}\:{u}\right) \\ $$$$\Rightarrow…

Find-minimum-value-of-function-f-x-4x-2-8x-13-6-1-x-

Question Number 135211 by benjo_mathlover last updated on 11/Mar/21 $$\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{4x}^{\mathrm{2}} +\mathrm{8x}+\mathrm{13}}{\mathrm{6}\left(\mathrm{1}+\mathrm{x}\right)} \\ $$ Commented by mr W last updated on 11/Mar/21 $$\underset{{x}\rightarrow−\mathrm{1}^{−} }…

Does-a-function-f-x-exist-such-that-for-f-n-x-d-n-f-dx-n-That-1-lim-n-k-f-n-x-k-and-2-lim-n-k-f-n-x-f-k-

Question Number 4118 by Filup last updated on 29/Dec/15 $$\mathrm{Does}\:\mathrm{a}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{exist} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{for} \\ $$$${f}^{\:\left({n}\right)} \left({x}\right)=\frac{{d}^{{n}} {f}}{{dx}^{{n}} } \\ $$$$\mathrm{That}: \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\underset{{n}\rightarrow{k}} {\mathrm{lim}}\:{f}^{\:\left({n}\right)} \left({x}\right)={k} \\ $$$$\boldsymbol{\mathrm{and}}…

nice-calculus-please-calculate-n-1-H-n-2-n-2-

Question Number 135143 by mnjuly1970 last updated on 10/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{nice}\:\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\:{please}\:\:{calculate}:\downarrow\downarrow\downarrow \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\::::\:\:\boldsymbol{\phi}\overset{??} {=}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} ^{\:^{\mathrm{2}} } }{{n}^{\mathrm{2}} }\:\: \\ $$$$\:\:\:\:\:\: \\ $$…

f-x-x-sin-x-x-g-x-x-Why-is-f-x-0-on-g-x-Are-all-extrema-min-max-inflection-of-f-x-on-g-x-

Question Number 4040 by Filup last updated on 27/Dec/15 $${f}\left({x}\right)={x}^{\mathrm{sin}^{{x}} \left({x}\right)} \\ $$$${g}\left({x}\right)={x} \\ $$$$ \\ $$$$\mathrm{Why}\:\mathrm{is}\:{f}\:'\left({x}\right)=\mathrm{0}\:\mathrm{on}\:{g}\left({x}\right)? \\ $$$$ \\ $$$${Are}\:\boldsymbol{{all}}\:{extrema}\:\left(\mathrm{min},\:\mathrm{max},\:\mathrm{inflection}\right) \\ $$$$\mathrm{of}\:{f}\left({x}\right)\:\mathrm{on}\:{g}\left({x}\right)? \\ $$…