Category: Differentiation

Question Number 131470 by bemath last updated on 05/Feb/21 $$Consideralargetankholding$$$$1000Lofpurewaterinto$$$$whichabrinesolutionof$$$$saltbeginstoflowatconstant$$$$rateof6L/min.Thesolution$$$$insidethetankiskeptwell$$$$stirredandisflowingoutof$$$${the}\:{tank}\:{at}\:{rate}\:{of}\:\mathrm{6}{L}/{min}. \…

Question Number 356 by 123456 last updated on 25/Jan/15 $$f_0\left(x\right)=1$$$$f_1\left(x\right)=x$$$$f_{n+1}\left(x\right)=x^{f_n\left(x\right)}$$$$\frac{\partial f_n}{\partial x}=?,n\in {\mathbb{N}}^{\ast }$$ Answered by…

Question Number 281 by samarth last updated on 25/Jan/15 $$\mathrm{If}f\left(x\right)={\tan }^{-1}\sqrt{\frac{1+\sin x}{1-\sin x}},0⩽x⩽\pi /2,\mathrm{then}f{}^{\prime }\left(\pi /6\right)=?$$ Answered by 123456 last updated on 18/Dec/14 $$f\left(x\right)={\tan }^{-1}\sqrt{\frac{1+\sin x}{1-\sin x}}$$$$\frac{\partial{f}}{\partial{x}}=\frac{\partial}{\partial{x}}\left(\mathrm{tan}^{−\mathrm{1}} \sqrt{\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{sin}\:{x}}}\right)…

Question Number 65651 by Masumsiddiqui399@gmail.com last updated on 01/Aug/19 Commented by Prithwish sen last updated on 01/Aug/19 $${(\mathrm{x}-1)}^2+{\mathrm{y}}^2=0\Rightarrow \mathrm{x}-1=0\mathrm{and}\mathrm{y}=0$$$$\therefore\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} =\mathrm{1} \…

Question Number 131121 by abdurehime last updated on 01/Feb/21 Answered by mathmax by abdo last updated on 01/Feb/21 $$\left.\mathrm{A}\right)\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\mathrm{25}\:\Rightarrow\mathrm{y}^{\mathrm{2}} \:=\mathrm{25}−\mathrm{x}^{\mathrm{2}} \:\Rightarrow\mathrm{y}=\xi\sqrt{\mathrm{25}−\mathrm{x}^{\mathrm{2}} }\left(\:\xi=\overset{−} {+}\mathrm{1}\right)\:\Rightarrow…