Category: Differentiation

Question Number 75793 by ~blr237~ last updated on 17/Dec/19 $$\mathrm{Prove}\mathrm{that}{\int }_0^{\mathrm{\infty }}{\left(\frac{\mathrm{arctanx}}{\mathrm{x}\sqrt{\log 2}}\right)}^2\mathrm{dx}=\pi$$ Commented by mathmax by abdo last updated on 18/Dec/19 $${let}\:{I}\:=\int_{\mathrm{0}}…

Question Number 75762 by aliesam last updated on 16/Dec/19 $$ifycos\left(x\right)+xcos\left(y\right)=\pi$$$$$$$$find\frac{d^{2}y}{{dx}^2},x=0$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 141274 by mnjuly1970 last updated on 17/May/21 $$\dots \dots .elementary\dots ..calculus\dots \dots ..$$$$iff\left(x\right):=\frac{\sqrt[3]{(x^3+x-2)(2x^2+x-3)(1-x^3)}}{{(2+cos\left(\pi x\right))}^3}$$$$thenf{}^{\prime }\left(0\right)=?\mathrm{\&}f{}^{\prime }\left(1\right)=?$$$$$$ Answered by mindispower…

Question Number 75639 by aliesam last updated on 14/Dec/19 Answered by $@ty@m123lastupdatedon14/Dec/19$$x=y\cos y\dots .\left(1\right)$$$\$Differentiatingw.r.t.x,$$$$1=\{y(-\sin y)+\cos y\}{y}^{\prime }$$$$\frac{1}{y^{\prime }}=\cos y-y\sin y\dots .\left(2\right)$$$${Multiplying}\:\left(\mathrm{2}\right)\:{by}\:{y},…

Question Number 141132 by mnjuly1970 last updated on 16/May/21 $$$$$$\dots mathematical\dots analysis\dots$$$$provethat:$$$$\underset{n=0}{\prod ^{\mathrm{\infty }}}(1+\frac{1}{2^{2^n}})\stackrel{?}{=}2$$$$\dots \dots$$…