Q61. Find the value of \(\frac{dy}{dx} \: \) if \(, \: y=x^{e^{x}}.\)

Q62. What is the value of \( \lim\limits_{x \to 4} \frac{x^2-2x-8}{x-4} ?\)

Q63. The equation of line joining \((3, 4)\) and \((5, 8)\) is \(_{-----------}\)

Q64. What is the median of the following data set : 32, 6, 21, 10, 8, 11, 12, 36, 17, 16, 15, 18, 40, 24, 21, 23, 24, 24, 29, 16, 32, 31, 10, 30, 35, 32, 18, 39, 12, 20

Q65. A particle is moving in a straight line and its distance \(d \: cm\) from a fixed point in the line after \(t \: seconds\) is given by \(d = 2t^3 – 12t + 7\). What is the velocity of the particle after \(4 \: seconds\)?

Q66. What is the value of \(\frac{d(\sin⁡ x^3 \: \cos⁡ x^2)}{dx} ?\)

Q67. In \(\int_{a}^{b} f(x) dx\), what is \('a'\) called as?

Q68. Find the \(log\) of \(64\) to the base \(4\).

Q69. What is the value of \( \lim\limits_{x \to 0} \frac{\sin{x}}{x} ?\)

Q70. What is the value of \(\frac{d}{dx}(ln (\frac{⁡5}{x}))?\)