How do you differentiate the following parametric equation: # (sint,cost-t)#?
1 Answer
Nov 16, 2016
# d/dt(sint,cost-t) = -tant -csct #
Explanation:
Define
#f(t) = (x(t), y(t))# where#{ (x(t)=sint,=>dx/dt=cost), (y(t)=cost-t,=>dy/dt=-sint-1) :} #
Then by the chain rule we have;
# f'(t) =dy/dx = dy/dt*dt/dx = (dy/dt) / (dx/dt) #
# :. dy/dx = (-sint-1) / (cost) #
# :. dy/dx = -sint/cost -1/cost #
# :. dy/dx = -tant -csct #
