How do you differentiate the following parametric equation: # x(t)=t-lnt, y(t)= cost-sint #?

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Answer 1 · 2016-02-07T15:40:20

#dy/dx=(sint+cost)*t/(1-t)#

Differentiate each function individually to obtain:

#dx/dt# and #dy/dt#

Then we can say:

#dy/dx = dy/dt*(dx/dt)^-1#

#dx/dt = 1-1/t =(t-1)/t -> (dx/dt)^-1 = t/(t-1)#
#dy/dt=-sint -cost#

Thus# dy/dx = dy/dt*(dx/dt)^-1 = (-sint-cost)*t/(t-1)#

#dy/dx=(sint+cost)*t/(1-t)#