Category: Differentiation

Question Number 134373 by mnjuly1970 last updated on 02/Mar/21 Answered by Dwaipayan Shikari last updated on 02/Mar/21 $${I}\left({a}\right)=\underset{{n}=−\infty} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({n}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}} }=\frac{\mathrm{1}}{{a}^{\mathrm{4}} }+\mathrm{2}\underset{{n}=\mathrm{1}} {\overset{\infty}…

Question Number 134285 by bramlexs22 last updated on 02/Mar/21 $$\mathrm{Find}\mathrm{maximum}\mathrm{value}\mathrm{of}$$$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{(16-{\mathrm{x}}^2)({\mathrm{x}}^2-9)}$$ Answered by EDWIN88 last updated on 02/Mar/21 $$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)=\left(\mathrm{16}−\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{x}^{\mathrm{2}}…

Question Number 134204 by liberty last updated on 01/Mar/21 $$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{2(1-\cos 2\mathrm{x})}.$$$$\mathrm{find}\mathrm{f}{}^{\prime }\left(0\right).$$ Answered by bramlexs22 last updated on 02/Mar/21 $$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{2\left(2\sin {}^2\mathrm{x}\right)}=\mid 4\sin \mathrm{x}\mid =2\mid \sin \mathrm{x}\mid$$$$\:\mathrm{f}\:'\left(\mathrm{0}^{−}…

Question Number 134108 by Eric002 last updated on 27/Feb/21 $$\frac{d}{dx}\left(\sqrt[4]{\frac{x^3+1}{x^3-1}}\right)$$ Answered by Ñï= last updated on 27/Feb/21 $$\frac{{d}}{{dx}}\left(\sqrt[{\mathrm{4}}]{\frac{{x}^{\mathrm{3}} +\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{1}}}\right) \…

Question Number 134040 by benjo_mathlover last updated on 27/Feb/21 $$\mathrm{Find}\mathrm{the}\mathrm{shortest}\mathrm{distance}$$$$\mathrm{between}\mathrm{the}\mathrm{curve}$$$${\mathrm{y}}^2=\mathrm{x}-1\mathrm{and}{\mathrm{x}}^2=\mathrm{y}-1$$ Commented by benjo_mathlover last updated on 27/Feb/21…