Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 125165 by Mammadli last updated on 08/Dec/20

$$\mathit{f}\left(\mathit{x}\right)={\mathit{s}\mathit{i}\mathit{n}\mathit{x}}^{\mathit{c}\mathit{o}\mathit{s}\mathit{x}}$$$$\mathit{f}{}^{\prime }\left(\mathit{x}\right)=?$$

Answered by Dwaipayan Shikari last updated on 08/Dec/20

$$f\left(x\right)={\left(sinx\right)}^{cosx}$$$$log\left(f\left(x\right)\right)=cosxlog\left(sinx\right)$$$$\frac{f^{\prime }\left(x\right)}{f\left(x\right)}=-sinxlog\left(sinx\right)+\frac{{cos}^{2}x}{sinx}$$$$f^{\prime }\left(x\right)={\left(sinx\right)}^{cosx}(log\left(\frac{1}{{\left(sinx\right)}^{sinx}}\right)+{\left(sinx\right)}^{cosx-1}{cos}^{2}x$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com