Category: Differentiation

Question Number 84442 by Power last updated on 13/Mar/20 Answered by john santu last updated on 13/Mar/20 $$\mathrm{let}\mathrm{y}={\mathrm{x}}^{{3\mathrm{x}}^{5\mathrm{x}}}\Rightarrow \ln \left(\mathrm{y}\right)=\ln \left({\mathrm{x}}^{{3\mathrm{x}}^{5\mathrm{x}}}\right)$$$$\mathrm{let}\:\mathrm{3x}^{\mathrm{5x}} \:=\:\mathrm{g}\left(\mathrm{x}\right)…

Question Number 18905 by Arnab Maiti last updated on 01/Aug/17 $$\mathrm{prove}\mathrm{that}\mathrm{the}\mathrm{differentiation}$$$$\mathrm{of}\frac{\sqrt{1+{\mathrm{x}}^2}-\sqrt{1-{\mathrm{x}}^2}}{\sqrt{1+{\mathrm{x}}^2}+\sqrt{1-{\mathrm{x}}^2}}\mathrm{with}\mathrm{respect}$$$$\mathrm{to}\sqrt{1-{\mathrm{x}}^4}\mathrm{is}\frac{\sqrt{1-{\mathrm{x}}^4}}{{\mathrm{x}}^6}$$ Terms…

Question Number 84326 by sahnaz last updated on 11/Mar/20 $$\int \frac{3-7\mathrm{u}}{{7\mathrm{u}}^2-7}\mathrm{du}$$ Answered by TANMAY PANACEA last updated on 11/Mar/20 $$\frac{\mathrm{3}}{\mathrm{7}}\int\frac{{du}}{\left({u}+\mathrm{1}\right)\left({u}−\mathrm{1}\right)}−\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{d}\left(\mathrm{7}{u}^{\mathrm{2}} −\mathrm{7}\right)}{\mathrm{7}{u}^{\mathrm{2}} −\mathrm{7}} \…

Question Number 84236 by niroj last updated on 10/Mar/20 $$\mathrm{If}{\mathbf{ax}}^2+2\mathbf{hxy}+{\mathbf{by}}^2=1,\mathrm{show}\mathrm{that}$$$$\frac{{\mathbf{d}}^2\mathbf{y}}{{\mathbf{dx}}^2}=\frac{{\mathbf{h}}^2-\mathbf{ab}}{{(\mathbf{hx}+\mathbf{by})}^3}.$$ Answered by TANMAY PANACEA last…

Question Number 84178 by www.abhisheksoni39@gmail.com last updated on 10/Mar/20 $$\mathrm{Find}\frac{dy}{dx}\mathrm{given}\mathrm{that}y=\left({sin}^{n}xcosnx\right)$$ Answered by john santu last updated on 10/Mar/20 $$\mathrm{using}\mathrm{product}\mathrm{rule}$$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{nsin}^{\mathrm{n}−\mathrm{1}} \left(\mathrm{x}\right)\:\mathrm{cos}\:\left(\mathrm{x}\right)\mathrm{cos}\:\left(\mathrm{nx}\right)+…