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Category: Differentiation

dx-dy-a-b-a-y-c-b-a-sin-2piy-c-2pi-for-a-gt-0-b-gt-0-c-gt-0-on-x-0-

Question Number 130087 by bobhans last updated on 22/Jan/21 $$\frac{{dx}}{{dy}}\:=\:{a}\:+\:\frac{\left({b}−{a}\right){y}}{{c}}\:+\:\frac{\left({b}−{a}\right)\mathrm{sin}\:\left(\frac{\mathrm{2}\pi{y}}{{c}}\right)}{\mathrm{2}\pi} \\ $$$${for}\:{a}>\mathrm{0}\:,\:{b}>\mathrm{0},\:{c}>\mathrm{0}\:{on}\:{x}\geqslant\mathrm{0}\: \\ $$ Answered by benjo_mathlover last updated on 22/Jan/21 $$\mathrm{dx}\:=\:\mathrm{a}\:\mathrm{dy}\:+\:\frac{\left(\mathrm{b}−\mathrm{a}\right)}{\mathrm{c}}\:\mathrm{y}\:\mathrm{dy}\:+\:\frac{\mathrm{b}−\mathrm{a}}{\mathrm{2}\pi}\:\mathrm{sin}\:\left(\frac{\mathrm{2}\pi\mathrm{y}}{\mathrm{c}}\right)\:\mathrm{dy} \\ $$$$\mathrm{x}=\:\mathrm{ay}\:+\frac{\left(\mathrm{b}−\mathrm{a}\right)\mathrm{y}^{\mathrm{2}} }{\mathrm{2c}}\:−\frac{\left(\mathrm{b}−\mathrm{a}\right)\mathrm{c}}{\mathrm{4}\pi^{\mathrm{2}}…

Question-64287

Question Number 64287 by aliesam last updated on 16/Jul/19 Commented by mathmax by abdo last updated on 16/Jul/19 $${R}^{'} \left({t}\right)\:=\frac{\mathrm{15}.\mathrm{0},\mathrm{01}\:{e}^{−\mathrm{0},\mathrm{01}{t}} \left(\mathrm{1}+\mathrm{1},\mathrm{5}{e}^{−\mathrm{0},\mathrm{01}{t}} \right)−\mathrm{15}\left(\mathrm{1}−{e}^{−\mathrm{0},\mathrm{01}{t}} \right)\left(−\mathrm{1},\mathrm{5}\right)\mathrm{0},\mathrm{01}\:{e}^{−\mathrm{0},\mathrm{01}{t}} }{\left(\mathrm{1}+\mathrm{1},\mathrm{5}\:{e}^{−\mathrm{0},\mathrm{01}{t}} \right)^{\mathrm{2}}…

Calculer-les-de-rive-es-n-ie-mes-en-0-de-la-fonction-de-finie-par-f-x-x-2-1-x-4-

Question Number 129815 by stelor last updated on 19/Jan/21 $$\mathrm{Calculer}\:\mathrm{les}\:\mathrm{d}\acute {\mathrm{e}riv}\acute {\mathrm{e}es}\:\mathrm{n}-\mathrm{i}\grave {\mathrm{e}mes}\:\mathrm{en}\:\mathrm{0}\:\mathrm{de}\: \\ $$$$\mathrm{la}\:\mathrm{fonction}\:\mathrm{d}\acute {\mathrm{e}finie}\:\mathrm{par}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{4}} } \\ $$ Answered by mathmax by abdo…