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f(x)=x^xln(cos(x)/((4-3x^2)^(1/2)))−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

ddx(xx)[ln (cosx4−3x2)]\frac{d}{dx}\left(x^x\right)\left[ln\:\left(\frac{cosx}{\sqrt{4-3x^2}}\right)\right]

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Final answer to the exercise

(ln⁡(x)+1)xx(ln⁡(cos⁡(x))−12ln⁡(4−3x2))+xx(−tan⁡(x)+3x4−3x2)\left(\ln\left(x\right)+1\right)x^x\left(\ln\left(\cos\left(x\right)\right)-\frac{1}{2}\ln\left(4-3x^2\right)\right)+x^x\left(-\tan\left(x\right)+\frac{3x}{4-3x^2}\right)

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ddx (xx)[ln (cosx√4−3x2 )]
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