Find the first derivative of the following functions using implicit differentiation:

$y^3-3x^2=6y-1$

If $s(t)=4t^3+8t-9$ is the distance in cm after $t$ seconds, find the acceleration at $1\mathrm{.}7$ seconds.

Given the function, $f(x)=4x^3-12x+3$ find the critical points:

A cube is measured at $10\mathrm{.}00$ cm with a possible error of $+-0\mathrm{.}03cm.$ Find the approx. error and $\%$ error in the volume.

Evaluate the following integrals.

$10.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}2x\sqrt[3]{9x^2-5}dx$