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

Exercise

ddx(xx)=ln⁡(x)sin⁡(x)\frac{d}{dx}\left(x^x\right)=\ln\left(x\right)^{\sin\left(x\right)}

Step-by-step Solution

1

The derivative ddx(xx)\frac{d}{dx}\left(x^x\right) results in (ln⁡(x)+1)xx\left(\ln\left(x\right)+1\right)x^x

(ln⁡(x)+1)xx=ln⁡(x)sin⁡(x)\left(\ln\left(x\right)+1\right)x^x=\ln\left(x\right)^{\sin\left(x\right)}

Final answer to the exercise

(ln⁡(x)+1)xx=ln⁡(x)sin⁡(x)\left(\ln\left(x\right)+1\right)x^x=\ln\left(x\right)^{\sin\left(x\right)}

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ddx (xx)=ln(x)sin(x)
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