(1)设$y=y(x)$由方程 $e^y 6xy x^2-1=0$ 确定，求 $y''(0)$.
(2)由方程$\sin xy \ln (y-x)=x$确定函数$y=y(x)$,求 $\frac {dy}{dx}|_{x=0}$.
(3)设$y=y(x)$是由 $e^{xy}-x y-2=0$确定的隐函数,求$y"(0)$.
(4)设 $\int _{0}^{x^{2}}te^{t}dt \int _{0}^{ \ln y}e^{t} \sqrt {1 t^{2}}dt=e^{x^{2}}$, 求 $\frac {dy}{dx}$.
(5)设 $\int _{1}^{y-x^{2}}e^{t^{2}}dt= \int _{0}^{x} \cos (x-t)^{2}dt$ 确定$y$为$x$的函数，求 $\frac {dy}{dx}$.
$\text{A.}$ 若 $\lim \limits _{x \rightarrow 0^{ }}f(x)=0$, 则 $\lim \limits _{x \rightarrow 0^{ }}f'(x)=0$
$\text{B.}$ 若 $\lim \limits _{x \rightarrow 0^{ }}f'(x)=0$, 则 $\lim \limits _{x \rightarrow 0^{ }}f(x)=0$
$\text{C.}$ 若 $\lim \limits _{x \rightarrow \infty }f(x)= \infty $, 则 $\lim \limits _{x \rightarrow \infty }f'(x)= \infty$
$\text{D.}$ 若 $\lim \limits {x \rightarrow \infty }f'(x)=A>0$, 则 $\lim \limits {x \rightarrow \infty }f(x)= \infty$