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Category: Differentiation

Differentiate-with-respect-to-x-arctan-a-2-x-2-a-2-x-2-

Question Number 45464 by peter frank last updated on 13/Oct/18 $$\boldsymbol{\mathrm{D}}\mathrm{ifferentiate}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\boldsymbol{\mathrm{x}} \\ $$$$\boldsymbol{\mathrm{arctan}}\left(\frac{\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right) \\ $$ Commented by peter frank last updated…

solve-the-simultaneous-equation-a-sin-x-y-1-2-cos2x-1-2-for-x-and-y-ranging-from-0-to-360-inclusive-b-if-siny-cosx-x-show-that-d-2-y-dx-2-x-2-x-2-3-2-

Question Number 45280 by peter frank last updated on 11/Oct/18 $$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{simultaneous}}\:\boldsymbol{\mathrm{equation}} \\ $$$$\left.\boldsymbol{\mathrm{a}}\right)\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\:\:\:} \\ $$$$\boldsymbol{\mathrm{cos}}\mathrm{2}\boldsymbol{\mathrm{x}}=\frac{-\mathrm{1}\:\:}{\mathrm{2}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{ranging}}\:\boldsymbol{\mathrm{from}}\:\mathrm{0}\:\boldsymbol{\mathrm{to}}\:\mathrm{360}\:\boldsymbol{\mathrm{inclusive}} \\ $$$$\left.\boldsymbol{\mathrm{b}}\right)\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{siny}}+\boldsymbol{\mathrm{cosx}}=\boldsymbol{\mathrm{x}}\:\:\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}\:} }\:=\frac{\boldsymbol{\mathrm{x}}}{\left(\mathrm{2}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$ Answered by…

Question-176274

Question Number 176274 by mnjuly1970 last updated on 15/Sep/22 Answered by Frix last updated on 16/Sep/22 $${y}=\mathrm{coth}\:{x}\:\Leftrightarrow\:{x}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\frac{{y}+\mathrm{1}}{{y}−\mathrm{1}} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{coth}^{−\mathrm{1}} \:\sqrt{\mathrm{2}}\:=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\mathrm{ln}\:\left(\mathrm{1}+\sqrt{\mathrm{2}}\right) \\ $$$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{\mathrm{sin}^{\mathrm{2}} \:{x}}{\:\sqrt{\mathrm{tan}^{\mathrm{2}}…

If-f-x-csc-pix-3-sec-pix-6-and-f-a-pi-9-Find-the-value-of-a-

Question Number 175952 by cortano1 last updated on 10/Sep/22 $$\:\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{csc}\:\left(\frac{\pi\mathrm{x}}{\mathrm{3}}\right)+\mathrm{sec}\:\left(\frac{\pi\mathrm{x}}{\mathrm{6}}\right) \\ $$$$\:\mathrm{and}\:\mathrm{f}\:'\left(\mathrm{a}\right)=\:−\frac{\pi}{\mathrm{9}}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{a}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

If-cos-x-dy-dx-y-y-pi-3-

Question Number 175879 by cortano1 last updated on 08/Sep/22 $$\:\:\mathrm{If}\:\mathrm{cos}\:\mathrm{x}\:.\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{y}\:\Rightarrow\mathrm{y}\left(\frac{\pi}{\mathrm{3}}\right)=? \\ $$ Commented by mr W last updated on 08/Sep/22 $$\frac{{dy}}{{y}}=\frac{{dx}}{\mathrm{cos}\:{x}} \\ $$$$\frac{{dy}}{{y}}=\frac{\mathrm{cos}\:{x}\:{dx}}{\mathrm{cos}^{\mathrm{2}} \:{x}} \\…

Question-44613

Question Number 44613 by tio_fernida03 last updated on 02/Oct/18 Commented by ajfour last updated on 02/Oct/18 $${no}\:{minimum}\:{nor}\:{maximum} \\ $$$${since}\:{for}\:{x}=\:−\mathrm{1}.\mathrm{42173},−\mathrm{0}.\mathrm{34566} \\ $$$${denominator}\:{of}\:{h}\left({x}\right)=\mathrm{0}. \\ $$ Terms of…