What is the derivative of #f(t) = (tcos^2t , t^2sin^2t-cost ) #?

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Answer 1 · 2017-03-23T16:30:25

#(dy)/(dx)=(t^2cost+2tcost+sint)/(cos^2t+2tsintcost)#

In parametric form of equation #f(t)=(x(t),y(t))#

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

Here #x(t)=tcos^2t# and #y=t^2sint-cost#

and therefore #(dx)/(dt)=cos^2t-txx2costxx(-sint)#

= #cos^2t+2tsintcost#

and #(dy)/(dt)=t^2cost+2tcost+sint#

Hence #(dy)/(dx)=(t^2cost+2tcost+sint)/(cos^2t+2tsintcost)#