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GUJCET · Maths · Continuity and Differentiability
\(\left\{\frac{d}{d x}\left(x^x+x^{x+1}+x^{x+2}\right)\right\}_{x=e}=\) _________.
- A \(e^e\left(1+4 e+2 e^2\right)\)
- B \(e^e\left(1+e^2+2 e\right)\)
- C \(e^e\left(2 e^2+4 e+3\right)\)
- D \(e^e\left(3 e^2+2 e+2\right)\)
Answer & Solution
Correct Answer
(C) \(e^e\left(2 e^2+4 e+3\right)\)
Step-by-step Solution
Detailed explanation
\(\frac{d}{dx}(x^x) = x^x(\ln x+1)\) \(\left.\frac{d}{dx}(x^x)\right|_{x=e} = e^e(\ln e+1) = e^e(1+1) = 2e^e\)
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