Find the derivative of $x^{5}(3-6x^{-9}).$

If $y = x + \frac{1}{x}$,then which among the following holds?

If $f: R \rightarrow R$ is defined by $f(x) = \begin{cases} \frac{x - 2}{x^2 - 3x + 2}, & x \in R - \{1, 2\} \\ 2, & x = 1 \\ 1, & x = 2 \end{cases}$,then $\lim_{x \rightarrow 2} \frac{f(x) - f(2)}{x - 2} = $

If $y = x^2 + \cos(2x) + e^{ax}$,then find $\frac{dy}{dx}$.

Differentiate the function with respect to $x$: $\sin (ax+b)$

If $y = \frac{x^{2/3} - x^{-1/3}}{x^{2/3} + x^{-1/3}}$,$x \neq 0$,then $(x+1)^2 y_1 = $