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Category: Differentiation

for-the-function-z-xtan-1-y-x-ysin-1-x-y-2-then-the-value-of-x-z-x-y-z-y-

Question Number 214726 by universe last updated on 18/Dec/24 $$\mathrm{for}\:\mathrm{the}\:\mathrm{function}\:{z}\:=\:{x}\mathrm{tan}^{−\mathrm{1}} \left(\frac{{y}}{{x}}\right)+{y}\mathrm{sin}^{−\mathrm{1}} \left(\frac{{x}}{{y}}\right)+\mathrm{2} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\frac{\partial{z}}{\partial{x}}+{y}\frac{\partial{z}}{\partial{y}}=?\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

For-what-values-of-k-does-the-equation-e-kx-3-x-have-only-one-solution-in-R-

Question Number 214335 by depressiveshrek last updated on 05/Dec/24 $$\mathrm{For}\:\mathrm{what}\:\mathrm{values}\:\mathrm{of}\:{k}\:\mathrm{does}\:\mathrm{the}\:\mathrm{equation} \\ $$$${e}^{{kx}} =\mathrm{3}\sqrt{{x}}\:\mathrm{have}\:\mathrm{only}\:\mathrm{one}\:\mathrm{solution}\:\mathrm{in}\:\mathbb{R}? \\ $$ Answered by mr W last updated on 06/Dec/24 $${y}={e}^{{kx}} \:{and}\:{y}=\mathrm{3}\sqrt{{x}}\:{should}\:{have}\:{only}…

Let-y-x-be-the-solution-of-diff-eq-y-cos-x-y-cos-x-y-0-0-Find-y-pi-6-

Question Number 214000 by golsendro last updated on 24/Nov/24 $$\:\:\mathrm{Let}\:\mathrm{y}\left(\mathrm{x}\right)\:\mathrm{be}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{diff}\:\mathrm{eq}. \\ $$$$\:\:\mathrm{y}\:'=\:\frac{\mathrm{cos}\:\mathrm{x}+\mathrm{y}}{\mathrm{cos}\:\mathrm{x}}\:,\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\:\:\mathrm{Find}\:\mathrm{y}\left(\frac{\pi}{\mathrm{6}}\right). \\ $$ Commented by mr W last updated on 24/Nov/24 $${do}\:{you}\:{mean}\:\mathrm{cos}\:\left({x}+{y}\right)\:{instead}\:{of}…

Question-212928

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} \\…

If-H-n-1-1-2-1-3-1-n-1-n-prove-that-n-1-H-n-ln-2-n-ln-2-2-

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

If-1-x-2-1-y-2-a-x-y-then-prove-that-dy-dx-1-y-2-1-x-2-

Question Number 211508 by MATHEMATICSAM last updated on 11/Sep/24 $$\mathrm{If}\:\sqrt{\mathrm{1}\:−\:{x}^{\mathrm{2}} }\:+\:\sqrt{\mathrm{1}\:−\:{y}^{\mathrm{2}} }\:=\:{a}\left({x}\:−\:{y}\right)\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{dy}}{{dx}}\:=\:\sqrt{\frac{\mathrm{1}\:−\:{y}^{\mathrm{2}} }{\mathrm{1}\:−\:{x}^{\mathrm{2}} }\:}\:. \\ $$ Commented by Frix last updated on 11/Sep/24…

If-f-x-x-2-g-x-sin-x-Then-find-df-dg-

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}'} \\…