How do you differentiate the following parametric equation: # x(t)=sqrt(t^2+tcos2t), y(t)=t^2sint #?

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Answer 1 · 2017-06-05T18:46:57

#dy/dx=((4tsint+2t^2cost)sqrt(t^2 + t cos2t))/(2 t - 2 t sin2t + cos2 t)#

The derivative of a parametric equation is given by the following formula:

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

#y(t)=t^2sint#

#dy/(dt)=2tsint+t^2cost#

#x(t)=sqrt(t^2+tcos2t)#

#dx/(dt)=(2t - 2t sin2t + cos2t)/(2 sqrt(t^2 + t cos2t))#

#dy/dx=2tsint+t^2cost divide(2 t - 2 t sin2t + cos2 t)/(2 sqrt(t^2 + t cos2 t))#

#=((4tsint+2t^2cost)sqrt(t^2 + t cos2t))/(2 t - 2 t sin2t + cos2 t)#