Question and Answers Forum

All Questions      Topic List

Differential Equation Questions

Previous in All Question      Next in All Question      

Previous in Differential Equation      Next in Differential Equation      

Question Number 19199 by priyankavarma094@gmail.com last updated on 06/Aug/17

$$\mathrm{y}=\tan {\mathrm{x}}^{\tan {\mathrm{x}}^{\tan \mathrm{x}}}$$

Answered by NEC last updated on 06/Aug/17

$$letu=\tan x$$$$$$$$y=u^{u^u}$$$$\ln y=u^u\ln u$$$$\frac{1}{y}dy/dx=u^u\left(\frac{1}{u}\right)+(u^u+\ln u)\ln u$$$$$$$$\frac{dy}{dx}=y\left[(u^u.\frac{1}{u}+(u^u+\ln u)\ln u)\right]$$$$\frac{dy}{dx}=\tan x{}^{\tan x{}^{\tan x}}\left\{(\tan x{}^{\tan x-1}+(\tan x{}^{\tan x}+\ln \tan x)\ln \tan x)\right\}$$

Commented by NEC last updated on 06/Aug/17

$$thatsifyouneeded\frac{dy}{dx}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com