x = t² - 1, y = (t-1)/(t+1), give x and y parametrically in terms of t? Compute dy/dx in terms of t?
I don't know how to combine x and y here...
does dy/dx mean i find d/dx of x, and d/dx of y, and then divide them?
Then it asks
"Find all values for t which dy/dx fails to exist"
When would a derivative fail to exist? when its not continuous? how can we find that?
Thanks...
Update:AAAND
it asks for
Find d/dt (dy/dx) ... is this
-cos t (2t + 1) - (-sin(t)) (2) / (2t + 1)²
= [2sin (t) - cos (t) (2t + 1)] / (2t + 1)??
then it says
find d/dx (dy/dx) ... what is this? I don't see an x in dy/dx...
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Verified answer
x = t²-1
dx/dt = 2t
y = (t-1)/(t+1)
dy/dt = (1(t+1) - 1(t-1))/(t+1)² = 2/(t+1)²
dy/dx = (dy/dt)/(dx/dt) = 1/(t(t+1)²)
dy/dx does not exist for
t=0
t = -1