Evaluate the following second derivative with respect to time, $t($note that $x$ is an unspecified function of time, i$.$e$.,x=x(t).$

$\frac{d^2}{d{t}^2}[(lnx)(cosx)(3x^4+2x^3)]$

For following function, find the partial fraction expansion.

$\frac{12x^3+10x^2+5x+3}{x^4+x^3+x^2+x}$

For $T(s),$ determine phase and determine log of the magnitude when $s=-2+3j($such that $s$ is a complex number with a real part of $-2$ and an imaginary part of $+3).$

$T(s)=\frac{3s+6}{3s^2+18s+108}$