How do you differentiate the following parametric equation: # (tsec(t/3-pi),t cos(pi-t))#?

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Answer 1 · 2018-08-09T01:55:39

#(dy)/(dx) = (cos^2t ( cos t - t sin t ))/( cos t + t sin t )#

#x = t sec( t/3 - pi ) = t sec ( pi - t ) = - t sec t#

#(dx)/(dt) = - sec t - t sec t tan t = - sec t ( 1 + t tan t )#

#y = t cos ( pi - t ) = - t cos t#

#(dy)/(dt) = - cos t + t sin t#

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

#= ( cos t - t sin t )/( sec t ( 1 + t tan t ))#

#= (cos^2t ( cos t - t sin t ))/( cos t + t sin t )#