How do you differentiate the following parametric equation: # x(t)=t-e^(t^2-t+1), y(t)= te^(t-t^2)#?
1 Answer
May 12, 2017
To differentiate
#x'(t)=1-e^(t^2-t+1)(d/dt(t^2-t+1))#
#color(white)(x'(t))=1-e^(t^2-t+1)(2t-1)#
And to differentiate
#y'(t)=(d/dt t)e^(t-t^2)+t(d/dte^(t-t^2))#
#color(white)(y'(t))=e^(t-t^2)+te^(t-t^2)(d/dt(t-t^2))#
#color(white)(y'(t))=e^(t-t^2)+te^(t-t^2)(1-2t)#
#color(white)(y'(t))=e^(t-t^2)(1+t(1-2t))#
#color(white)(y'(t))=e^(t-t^2)(1+t-2t^2)#
