Compute the derivative of $6 x^{100}-x^{55}+x$.

The derivative of $f(x) = |x^2 - x|$ at $x = 2$ is

If $f(x) = \frac{x}{1 + |x|}$ for $x \in R$,then $f'(0) = $

If $f(x) = \frac{x}{1+|x|}$,for $x \in \mathbb{R}$,then $f^{\prime}(0)$ is equal to :

If $y = \cos(x^{\circ})$ and $z = \cos x$,then $\frac{dy}{dz}$ is equal to

Let $f: R \rightarrow R$ satisfy the equation $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in R$ and $f(x) \neq 0$ for any $x \in R$. If the function $f$ is differentiable at $x=0$ and $f'(0)=3$,then $\lim_{h \rightarrow 0} \frac{1}{h}(f(h)-1)$ is equal to ....... .