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Category: Differentiation

find-dy-dx-of-ln-sechx-lnlnx-

Question Number 2484 by John_Haha last updated on 21/Nov/15 $${find}\:{dy}/{dx}\:{of}\:{ln}\left({sechx}+{lnlnx}\right) \\ $$ Answered by Filup last updated on 21/Nov/15 $${y}=\mathrm{ln}\left(\mathrm{sech}\left({x}\right)+\mathrm{ln}\left(\mathrm{ln}\left({x}\right)\right)\right) \\ $$$$ \\ $$$$\frac{{dy}}{{dx}}=\frac{{d}\left(\mathrm{ln}\left(\mathrm{u}\right)\right)}{\mathrm{d}{x}}\:\frac{{du}}{{dx}}\:\:\:\:\:\:\:\:\:\left({chain}\:{rule}\right) \\…

d-dx-tan-1-4x-1-4x-2-or-d-dx-tan-1-2tan-where-2x-sin-which-comes-later-if-done-considering-2x-sin-please-help-

Question Number 67960 by aseer imad last updated on 02/Sep/19 $$\frac{{d}}{{dx}}\left[{tan}^{−\mathrm{1}} \frac{\mathrm{4}{x}}{\:\sqrt{\mathrm{1}−\mathrm{4}{x}^{\mathrm{2}} }}\right] \\ $$$${or} \\ $$$$\frac{{d}}{{dx}}{tan}^{−\mathrm{1}} \left(\mathrm{2}{tan}\theta\right)\:\:\:\:\:\:\:\left[{where}\:\mathrm{2}{x}={sin}\theta\:\right] \\ $$$$\:\:\:{which}\:{comes}\:{later}\:{if}\:{done}\:{considering} \\ $$$$\mathrm{2}{x}={sin}\theta \\ $$$${please}\:{help} \\…

use-Green-Riemann-formuler-to-determined-I-D-xydxdy-D-x-y-R-2-x-0-y-x-y-1-

Question Number 67946 by Cmr 237 last updated on 02/Sep/19 $$\mathrm{use}\:\boldsymbol{\mathrm{Green}}−\boldsymbol{\mathrm{Riemann}}\:\boldsymbol{\mathrm{formuler}} \\ $$$$\mathrm{to}\:\mathrm{determined}: \\ $$$$\boldsymbol{\mathrm{I}}=\int\int_{\boldsymbol{\mathrm{D}}} \boldsymbol{\mathrm{xy}}\mathrm{dxdy} \\ $$$$\boldsymbol{\mathrm{D}}=\left\{\left(\mathrm{x},\mathrm{y}\right)\in\mathbb{R}^{\mathrm{2}} \mid\mathrm{x}\geqslant\mathrm{0};\mathrm{y}\geqslant;\mathrm{x}+{y}\leqslant\mathrm{1}\right\} \\ $$ Commented by mathmax by…

nice-calculus-prove-that-cosh-px-cosh-x-pi-cos-pip-2-

Question Number 133334 by mnjuly1970 last updated on 21/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:\:\:\:\:{calculus}… \\ $$$$\:{prove}\:\:{that}:: \\ $$$$\:\:\:\boldsymbol{\phi}=\int_{−\infty} ^{\:+\infty} \frac{\:{cosh}\left({px}\right)}{{cosh}\left({x}\right)}\:=\:\frac{\pi}{{cos}\left(\frac{\pi{p}}{\mathrm{2}}\right)} \\ $$$$ \\ $$ Answered by mnjuly1970 last updated…

f-x-x-2-3x-10-f-x-2x-3-and-f-1-5-what-indicate-these-vslue-f-x-andf-1-in-geometrical-meaning-

Question Number 2229 by tabrez8590@gmail last updated on 09/Nov/15 $${f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{10} \\ $$$$\Rightarrow{f}^{'} \left({x}\right)=\mathrm{2}{x}+\mathrm{3}\:{and} \\ $$$${f}^{'} \left(\mathrm{1}\right)=\mathrm{5}\:{what}\:{indicate}\:{these}\:{vslue}\: \\ $$$${f}'\left({x}\right){andf}'\left(\mathrm{1}\right)\:{in}\:{geometrical}\:{meaning} \\ $$ Answered by prakash jain…

it-is-necessary-for-diffrentiable-function-itmust-becontinuty-why-and-how-please-explain-by-example-

Question Number 2219 by tabrez8590@gmail last updated on 09/Nov/15 $${it}\:{is}\:{necessary}\:{for}\:{diffrentiable}\:\:{function}\:{itmust}\:{becontinuty}\:{why}?{and}\:{how}\:{please}\:{explain}\:{by}\:{example} \\ $$$$ \\ $$ Answered by Filup last updated on 09/Nov/15 $$\mathrm{if}\:\begin{cases}{{y}={x}\:\:\:\mathrm{if}\:{x}>\mathrm{0}}\\{{y}=−{x}\:\:\:\mathrm{if}\:{x}<\mathrm{0}}\end{cases} \\ $$$$ \\…