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

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Answer 1 · 2016-05-07T14:23:41

#(dy)/(dx)=(sint(2tsint+2t^2cost+1))/(e^t(1+t))#

When equation are given in parametric form such as

#x(t)=te^t# and #y(t)=t^2sin^2t-cost#

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

#(dy)/(dt)=2tsin^2t+t^2*2sintcost+sint#

#(dx)/(dt)=e^t+te^t=e^t(1+t)#

Hence #(dy)/(dx)=(2tsin^2t+t^2*2sintcost+sint)/(e^t(1+t))#

= #(sint(2tsint+2t^2cost+1))/(e^t(1+t))#