Question:
If \(y = x^x\), then what is the value of \(\dfrac{dy}{dx}\) at x = 1?
यदि \(y = x^x\) है, तो x = 1 पर \(\dfrac{dy}{dx}\) का मान क्या है?
Options:
- 0
- 1
- 2
- -1
- 0
- 1
- 2
- -1
Correct Answer: b)
Explanation:
\(y = x^x \implies \dfrac{dy}{dx} = x^x(1 + \ln x)\).
At \(x = 1\): \(\dfrac{dy}{dx} = 1^1(1 + \ln 1) = 1\).
\(y = x^x \implies \dfrac{dy}{dx} = x^x(1 + \ln x)\)। \(x = 1\) पर मान \(1\) है।