Category: Differentiation

Question Number 212928 by efronzo1 last updated on 27/Oct/24 Commented by mr W last updated on 27/Oct/24 $${does}\:{the}\:{question}\:{mean}\:{msximum} \\ $$$${or}\:{minimum}?\:{if}\:{C}\:{and}\:{D}\:{must}\:{lie} \\ $$$${between}\:{B}\:{and}\:{E},\:{then}\:{there}\:{is}\:{only} \\ $$$${min}\left({x}+{y}\right),\:{but}\:{no}\:{max}\left({x}+{y}\right).\:{if}\:{C} \\…

Question Number 211594 by mnjuly1970 last updated on 14/Sep/24 $$ \\ $$$$\:{If}\:,\:\:\overset{\:\:−} {{H}}_{{n}} \:=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}}\:−…+\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{{n}}\:\:\: \\ $$$${prove}\:{that}:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\overset{\:\:−\:} {{H}}_{{n}} −\mathrm{ln}\left(\mathrm{2}\right)}{{n}}=\mathrm{ln}^{\mathrm{2}} \left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:\:−−−−−−−−−−\:\:\:\:\:\: \\…

Question Number 211502 by MathematicalUser2357 last updated on 11/Sep/24 $$\mathrm{If}\:\begin{cases}{{f}\left({x}\right)={x}^{\mathrm{2}} }\\{{g}\left({x}\right)=\mathrm{sin}\:{x}}\end{cases}, \\ $$$$\mathrm{Then}\:\mathrm{find}\:\frac{{df}}{{dg}}. \\ $$ Answered by a.lgnaoui last updated on 11/Sep/24 $$\frac{\mathrm{df}}{\mathrm{dg}}=\frac{\mathrm{df}}{\mathrm{dx}}×\frac{\mathrm{dx}}{\mathrm{dg}}.=\:\:\frac{\mathrm{f}^{'} }{\mathrm{g}'} \\…

Question Number 211365 by JuniorKepler last updated on 06/Sep/24 Answered by mr W last updated on 07/Sep/24 $$\frac{\left({x}+{y}\right)^{{p}} \left({x}+{y}\right)^{{q}} }{{x}^{{p}} {y}^{{q}} }=\mathrm{1} \\ $$$$\left(\mathrm{1}+\frac{{y}}{{x}}\right)^{{p}} \left(\mathrm{1}+\frac{{x}}{{y}}\right)^{{q}}…

Question Number 210702 by depressiveshrek last updated on 17/Aug/24 $$\mathrm{How}\:\mathrm{many}\:\mathrm{real}\:\mathrm{solutions}\:\mathrm{does}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{x}=\mathrm{sin3}{x}\:\mathrm{have}? \\ $$ Answered by Frix last updated on 17/Aug/24 $${x}=\mathrm{sin}\:\mathrm{3}{x} \\ $$$${t}=\mathrm{3}{x} \\…