How do you differentiate the following parametric equation: # x(t)=e^tsint, y(t)= tcost-tsin^2t #?
1 Answer
Aug 6, 2017
# dy/dx = (cost -tsint - 2tsintcost-sin^2t) / (e^t(sint+cost)) #
Explanation:
We have:
# x = e^tsint #
# y = tcost-tsin^2t #
Differentiating wrt
# dx/dt = (e^t)(d/tsint) + (d/dte^t)(sint) #
# " " = (e^t)(cost) + (e^t)(sint) #
# " " = e^t(sint+cost) #
# dy/dt = (t)(d/dtcost) + (d/dtt)(cost) - {(t)(d/dtsin^2t)+(d/dtt)(sin^2t) #
# " " = (t)(-sint) + (1)(cost) - {(t)(2sintcost)+(1)(sin^2t) #
# " " = -tsint + cost - 2tsintcost-sin^2t #
By the chain rule we have:
# dy/dx = (dy//dt) / (dx//dt) #
# " " = (cost -tsint - 2tsintcost-sin^2t) / (e^t(sint+cost)) #
