If $f(x)$, defined by $f(x)=\left\{\begin{array}{lll}k x+1 & \text { if } & x \leq \pi \\ \cos x & \text { if } & x>\pi\end{array}\right.$ is continuous at $x=\pi$, then the value of $k$ is :

If $y = x^x$, $\frac{dy}{dx}$ will be:

If $y = \sin^{-1}x$, then $(1-x^2)\frac{d^2y}{dx^2}$ is equal to

If $e^x + e^y = e^{x+y}$, then $\frac{dy}{dx}$ =

The function $f(x) = |x - 1|$ is

If $y = (\log_e x)^{\log_e x}$, then $\dfrac{dy}{dx}$ is equal to:

If the function $f(x) = \begin{cases}\frac{\sin 3x}{x}, & \text{if } x \neq 0\\ \frac{3k}{2}, & \text{if } x = 0\end{cases}$ is continuous at $x = 0$, then the value of $k$ is