Assuming That the Equations Define X and Y Implicitly as Differentiable

Multiple Choice

Assuming that the equations define x and y implicitly as differentiable functions x = f(t) , y = g(t) , find the slope of the curve x = f(t) , y = g(t) at the given value of t.
- $$x = t \sin t + t , y \cos t + y = 2 t , t = \frac { \pi } { 2 }$$

A) $\frac { 2 + \pi } { 2 }$
B) $\frac { 2 } { 2 + \pi }$
C) $2 + \pi$
D) $- \frac { 2 } { 2 + \pi }$