Menu Close

Category: Differentiation

find-minimum-value-of-f-x-4sin-2x-5sin-x-5cos-x-6-

Question Number 164716 by cortano1 last updated on 21/Jan/22 $$\:\:\:{find}\:{minimum}\:{value}\:{of}\: \\ $$$$\:{f}\left({x}\right)=\mathrm{4sin}\:\mathrm{2}{x}−\mathrm{5sin}\:{x}−\mathrm{5cos}\:{x}+\mathrm{6} \\ $$ Answered by bobhans last updated on 21/Jan/22 $$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{4cos}\:\left(\frac{\pi}{\mathrm{2}}−\mathrm{2x}\right)−\mathrm{5}\sqrt{\mathrm{2}}\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{4}}−\mathrm{x}\right)+\mathrm{6} \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{4cos}\:\mathrm{2}\left(\frac{\pi}{\mathrm{4}}−\mathrm{x}\right)−\mathrm{5}\sqrt{\mathrm{2}}\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{4}}−\mathrm{x}\right)+\mathrm{6} \\…

solve-0-1-ln-2-x-tanh-1-x-x-dx-0-1-tanh-1-x-2-1-x-

Question Number 164653 by mnjuly1970 last updated on 20/Jan/22 $$ \\ $$$$\:\:\:\:\:\:\:\:{solve} \\ $$$$\:\:\boldsymbol{\phi}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}^{\:\mathrm{2}} \left(\:{x}\:\right).\:{tanh}^{\:−\mathrm{1}} \left(\:{x}\:\:\right)}{{x}}{dx}\:=? \\ $$$$\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\left({tanh}^{−\mathrm{1}} \left({x}\right)\right)^{\:\mathrm{2}} }{\mathrm{1}+{x}}\:=\:? \\…

Given-5x-3y-6-find-min-value-of-x-1-2-y-1-2-

Question Number 99003 by bramlex last updated on 18/Jun/20 $${Given}\:\mathrm{5}{x}−\mathrm{3}{y}=\mathrm{6}\:.\:{find}\:{min}\:{value} \\ $$$${of}\:\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\left({y}+\mathrm{1}\right)^{\mathrm{2}} \:? \\ $$ Answered by bobhans last updated on 18/Jun/20 $$\mathrm{let}\:\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{y}+\mathrm{1}\right)^{\mathrm{2}}…

if-y-x-find-dy-dx-

Question Number 33407 by NECx last updated on 15/Apr/18 $${if}\:{y}={x}!\:{find}\:{dy}/{dx} \\ $$ Answered by MJS last updated on 15/Apr/18 $$\mathrm{for}\:{x}\in\mathbb{N}\:\mathrm{no}\:\mathrm{derivate}\:\mathrm{exists} \\ $$$$\mathrm{if}\:\mathrm{we}\:\mathrm{use} \\ $$$${y}={x}!=\Gamma\left({x}\right)=\underset{\mathrm{0}} {\overset{\infty}…