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

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Answer 1 · 2017-10-30T19:25:46

#dy/dx = (e^t-cost)/(e^tcost - e^tsint -1# in terms of #t#

We can compute this via noting how;

#(dy/dt) / (dx/dt) #= #(dy)/dx#

Hence #dy/dx# = #(y'(t))/(x'(t))#

Hence #x'(t) = dx/dt = e^tcost - e^tsint - 1# by considering chain rule and product rule

and #y'(t) = dy/dt= e^t - cost#

Hence yielding;

#(y'(t))/(x'(t)) = dy/dx = (e^t-cost)/(e^tcost - e^tsint -1# in terms of #t#