The function $f(x)=\begin{cases}\frac{e^{3x}-e^{-5x}}{x}, & x\neq 0\\ \lambda, & x=0\end{cases}$ is continuous at x=0 for the value of '$\lambda$' as:

If $x = e^{\cos 2t}$, $y = e^{\sin 2t}$, then $\frac{dy}{dx}$ equals to

If $x\sqrt{1 + y} + y\sqrt{1 + x} = 0$, where $|x| < 1, |y| < 1$ and $x ≠ y$, then

Let $x=at^2, y=2at$. If $\frac{d^2y}{dx^2}+\frac{dy}{dx}=0$ at $t=3$, then $a$ is equal to:

At $x = 2$, $f(x) = [x]$ is

[where [.] is greatest integer function]

If $y = \frac{1}{x+1}$, then $\frac{d^2y}{dx^2}$ at $x = 2$ is:

The derivative of $(\log x)^x$ with respect to $\log x$ is