CUET · MATHS · PYQ PAPER 2023
If \(y=x^x, \frac{d y}{d x}\) will be:
- A \(x^x\)
- B \(x^x(1+\log x)\)
- C \(x^{x-1}\)
- D \(x^x+1\)
Answer & Solution
Correct Answer
(B) \(x^x(1+\log x)\)
Step-by-step Solution
Detailed explanation
\(\ln y = x \ln x\) \(\frac{1}{y} \frac{d y}{d x} = \ln x + 1\) \(\frac{d y}{d x} = y(1+\ln x)\) \(\frac{d y}{d x} = x^x(1+\ln x)\)
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