Question

How do you differentiate the following parametric equation: `x(t)=(t+1)^2+e^t, y(t)= (t-2)^2+t`?

Answer 1

`d y=((2(t-2)+1) /(2(t+1)+e^t*l n e))*d x`

Explanation:

`(d x)/(d t)=2*(t+1)*1+e^t*l n e=2(t+1)+e^t*l n e`

`(d y)/( d t)=2*(t-2)*1+1=`2(t-2)+1

`(d y)/(d x)=(d y)/(d t)*(d t)/(d x)=[2(t-2)+1] /(2(t+1)+e^t*l n e)`

`d y=((2(t-2)+1) /(2(t+1)+e^t*l n e))*d x`