How do you differentiate the following parametric equation: $x(t)=3(t+1)^2+2e^t, y(t)= (t+2)^2+t^2$ ?

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Answer 1 · 2015-12-03T19:18:11

$(dy)/(dx) = (3(t+1))/(2t+1)$

Step 1: Find $(dx)/(dt)$
Step 2: Find $(dy)/(dt)$
3) Step 3: $(dy)/(dt) = (dx)/(dt) * (dy)/(dx) hArr (dy)/(dx)= [(dy)/(dt)]/[(dx)/(dt)]$

Step 1: Given $x(t)= 3(t+1)^2$
$x'(t) = (dx)/(dt)= 3(2)(t+1)(1)$

$color(red)((dx)/(dt)= 6(t+1))$

Step 2: Given $y(t)= (t+2)^2 +t^2$
$y'(t) = (dy)/(dt)= 2(t+2)(1)+2t$

$(dy)/(dt)= 2t+4+2t = 4t+2$
$color(blue)((dy)/(dt)= 4t+2 = 2(2t+1))$

Step 3: $(dy)/(dt) = (dx)/(dt) * (dy)/(dx) hArr (dy)/(dx)= [(dy)/(dt)]/[(dx)/(dt)]$

$(dy)/(dx)= color(red)(6(t+1))/color(blue)(2(2t+1))$

$(dy)/(dx) = (3(t+1))/(2t+1)$

How do you differentiate the following parametric equation: x(t)=3(t+1)^2+2e^t, y(t)= (t+2)^2+t^2 x(t)=3(t+1)^2+2e^t, y(t)= (t+2)^2+t^2?