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Category: Differentiation

if-y-x-find-dy-dx-

Question Number 33407 by NECx last updated on 15/Apr/18 $${if}\:{y}={x}!\:{find}\:{dy}/{dx} \\ $$ Answered by MJS last updated on 15/Apr/18 $$\mathrm{for}\:{x}\in\mathbb{N}\:\mathrm{no}\:\mathrm{derivate}\:\mathrm{exists} \\ $$$$\mathrm{if}\:\mathrm{we}\:\mathrm{use} \\ $$$${y}={x}!=\Gamma\left({x}\right)=\underset{\mathrm{0}} {\overset{\infty}…

d-dx-e-tan-x-Z-A-

Question Number 164366 by Zaynal last updated on 16/Jan/22 $$\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\:\left(\boldsymbol{{e}}^{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)} \right) \\ $$$$\left\{\boldsymbol{{Z}}.\boldsymbol{\mathrm{A}}\right\} \\ $$ Commented by cortano1 last updated on 16/Jan/22 $$\:{y}\:=\:{e}^{\mathrm{tan}\:{x}} \\ $$$$\:\mathrm{ln}\:{y}\:=\:\mathrm{tan}\:{x}…

In-AB-C-cos-2-A-cos-2-B-cos-2-C-1-Prove-that-AB-C-is-right-angled-

Question Number 164339 by mnjuly1970 last updated on 16/Jan/22 $$ \\ $$$$\:\:\:\:{In}\:\:{A}\overset{\Delta} {{B}C}\:\:\::\:\:\:{cos}^{\:\mathrm{2}} \left({A}\:\right)+\:{cos}^{\:\mathrm{2}} \left({B}\:\right)+\:{cos}^{\:\mathrm{2}} \left(\:{C}\:\right)=\mathrm{1}\:\:. \\ $$$$\:\:\:\:\:\:\:\:{Prove}\:{that}\:\:{A}\overset{\Delta} {{B}C}\:\:\:{is}\:\:\:{right}\:{angled}. \\ $$$$\:\:\:\:\:\:−−−−−−−− \\ $$$$\:\:\:\:\:\: \\ $$…

let-considere-f-and-u-differenciable-function-prove-that-d-dt-a-u-t-f-t-x-dx-a-u-t-f-t-t-x-dx-f-t-u-t-u-t-

Question Number 33122 by abdo imad last updated on 10/Apr/18 $${let}\:{considere}\:{f}\:{and}\:{u}\:{differenciable}\:{function}\:{prove} \\ $$$${that}\:\frac{{d}}{{dt}}\left(\:\int_{{a}} ^{{u}\left({t}\right)} {f}\left({t},{x}\right){dx}\right)=\int_{{a}} ^{{u}\left({t}\right)} \:\frac{\partial{f}}{\partial{t}}\left({t},{x}\right){dx}\:+{f}\left({t},{u}\left({t}\right)\right){u}^{'} \left({t}\right) \\ $$ Terms of Service Privacy Policy…