$\left\{\frac{d}{d x}\left(\sec x^{\circ}\right)\right\}_{x=30} = $ . . . . . . .

Let $f(x) = \sum_{k=1}^{10} kx^k$,$x \in R$. If $2f(2) + f'(2) = 119(2)^n + 1$,then $n$ is equal to $..........$.

Let $f: \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \rightarrow \mathbb{R}$ be a differentiable function such that $f(0)=\frac{1}{2}$. If $\lim _{x \rightarrow 0} \frac{x \int_0^x f(t) dt}{e^{x^2}-1}=\alpha$,then $8 \alpha^2$ is equal to:

If $f(x) = e^{x} g(x)$,$g(0) = 2$,and $g^{\prime}(0) = 1$,then $f^{\prime}(0)$ is

At $x = \sqrt{\frac{\pi}{2}}$,find the value of $\frac{d}{dx} \cos(\sin(x^2))$.

If $[x]$ represents the greatest integer function and $f(x) = x - [x] - \cos x$,then $f^{\prime}\left(\frac{\pi}{2}\right) = $