List of top Mathematics Questions on limits and derivatives asked in Bihar Board XII

Find the derivative of \[ \frac{d}{dx} \left( \lim_{n \to 1} \frac{x^n - 1}{n+1} \right). \]
Find the derivative: \[ \frac{d}{dx} \left[ \left| \frac{x}{4} \right| \right] \]
Find the derivative of \( \log(x^9) \).
\(\frac{d}{dx} \left[ \log x^2 + \log a^2 \right] \)