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y-f-x-y-

Question Number 45776 by Sanjarbek last updated on 16/Oct/18 $$\boldsymbol{{y}}=\mid\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\mid \\ $$$$\boldsymbol{{y}}'−? \\ $$ Commented by maxmathsup by imad last updated on 16/Oct/18 $${for}\:{f}\left({x}\right)\neq\mathrm{0}\:{we}\:{have}\:\mid{f}\left({x}\right)\mid=\sqrt{{f}^{\mathrm{2}} \left({x}\right)}\:\Rightarrow\frac{{d}}{{dx}}\left(\mid{f}\left({x}\right)\mid\right)=\frac{\mathrm{2}{f}\left({x}\right){f}^{'}…

Question-111216

Question Number 111216 by mohammad17 last updated on 02/Sep/20 Commented by Dwaipayan Shikari last updated on 02/Sep/20 $${x}^{{y}} ={e}^{{tan}^{−\mathrm{1}} {y}} \\ $$$${ylogx}={tan}^{−\mathrm{1}} {y} \\ $$$$\frac{{dy}}{{dx}}{logx}+\frac{{y}}{{x}}=\frac{\mathrm{1}}{\mathrm{1}+{y}^{\mathrm{2}}…

dx-x-3-3x-5-

Question Number 111206 by mohammad17 last updated on 02/Sep/20 $$\int\:\frac{{dx}}{{x}^{\mathrm{3}} +\mathrm{3}{x}−\mathrm{5}} \\ $$ Answered by Sarah85 last updated on 02/Sep/20 $$\mathrm{we}\:\mathrm{had}\:\mathrm{this}\:\mathrm{before} \\ $$$$\mathrm{if}\:\mathrm{we}\:\mathrm{cannot}\:\mathrm{find}\:“\mathrm{nice}''\:\mathrm{factors}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{denominator}\:\mathrm{it}'\mathrm{s}\:\mathrm{getting}\:\mathrm{complicated}…