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

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Answer 1 · 2016-01-05T04:50:53

Explanation is given below.

#x(t) =e^(t^2-t)#
#y(t) = t^2 -t#

To find the derivative #dy/dx# we need to find #y'(t)# and #x'(t)#

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

#x(t)= e^(t^2-t)#
Differentiating with respect to #t#

#x'(t) = e^(t^2-t)d/dt(t^2-t)#
#x'(t)=e^(t^2-t)(2t-1)#
#x'(t)=(2t-1)e^(t^2-t)#

#y(t)=t^2-t#
Differentiating with respect to #t#

#y'(t)=2t-1#

#dy/dx = (2t-1)/((2t-1)e^(t^2-t))#
#dy/dx = cancel(2t-1)/(cancel(2t-1)e^(t^2-t))#

#dy/dx = 1/e^(t^2-t) #