text: # How do you differentiate the following parametric equation:  x(t)=(t+1)^2+e^t, y(t)= (t-2)^2+t?
  
  May 27, 2016
  
  $d y = \left(\frac{2 \left(t - 2\right) + 1}{2 \left(t + 1\right) + {e}^{t} \cdot l n e}\right) \cdot d x$
  
  #### Explanation:
  
  $\frac{d x}{d t} = 2 \cdot \left(t + 1\right) \cdot 1 + {e}^{t} \cdot l n e = 2 \left(t + 1\right) + {e}^{t} \cdot l n e$
  
  $\frac{d y}{d t} = 2 \cdot \left(t - 2\right) \cdot 1 + 1 =$2(t-2)+1
  
  $\frac{d y}{d x} = \frac{d y}{d t} \cdot \frac{d t}{d x} = \frac{2 \left(t - 2\right) + 1}{2 \left(t + 1\right) + {e}^{t} \cdot l n e}$
  
  $d y = \left(\frac{2 \left(t - 2\right) + 1}{2 \left(t + 1\right) + {e}^{t} \cdot l n e}\right) \cdot d x$