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.
- $x \cos t + x = 2 t , y = t \sin t + t , t = \frac { \pi } { 2 }$

A) 2
B) $\frac { 1 } { 1 + \pi }$
C) $2 + \pi$
D) $\frac { 2 } { 2 + \pi }$