If $f(x) = \begin{cases} \frac{x^2-16}{x-4} & \text{if } x > 4 \\ 2x & \text{if } x \leq 4 \end{cases}$ then $f^{\prime}(4^{-}) + f^{\prime}(4^{+}) = $

If $y=(1+x)(1+x^2)(1+x^4) \dots (1+x^{2^n})$,then $\left(\frac{dy}{dx}\right)_{x=0}$ is equal to

If $f^{\prime}(x)=k(\cos x-\sin x)$,$f^{\prime}(0)=3$,and $f\left(\frac{\pi}{2}\right)=15$,then $f(x)=$

If $y = t^{4/3} - 3t^{-2/3}$,then $\frac{dy}{dt} = $

If $f(1)=1$ and $f^{\prime}(1)=3$,then the derivative of $f(f(f(x)))+(f(x))^2$ at $x=1$ is

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} = $