If $y=(x-1)(x+2)(x^2+5)(x^4+8)$,then $\lim _{x \rightarrow-1}(\frac{d y}{d x})=$

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 $y = \frac{x}{2}\sqrt{a^2 + x^2} + \frac{a^2}{2}\log(x + \sqrt{x^2 + a^2})$,then $\frac{dy}{dx} = $

If $y=a \sin x+b \cos x$ (where $a$ and $b$ are constants),then $y^2+\left(\frac{d y}{d x}\right)^2$ is

Let $f(x) = \mathop {\text{Lim}}\limits_{h \to 0} \frac{1}{h} \int\limits_x^{x + h} \frac{dt}{t + \sqrt{1 + t^2}}$,then $\mathop {\text{Lim}}\limits_{x \to -\infty} x \cdot f(x)$ is

If $y = \sin [\cos (\sin x)],$ then $dy/dx = $