Question 95

The first derivative of $$x^{x}$$ is

Solution

Let us assume $$T=x^x$$

Taking log on both sides:

$$\log T=x\log x$$

$$\dfrac{1}{T}\left(\dfrac{dT}{dx}\right)=x\cdot\dfrac{1}{x}+\log x$$

$$\dfrac{dT}{dx}=x^x\left(1+\log x\right)$$

=> Option D is the correct answer.

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