How do you find #dy/dx# for the curve #x=t*sin(t)#, #y=t^2+2# ?
1 Answer
Aug 28, 2014
To find the derivative of a parametric function, you use the formula:
#dy/dx = (dy/dt)/(dx/dt)# , which is a rearranged form of the chain rule.
To use this, we must first derive
#y=t^2 + 2#
#dy/dt = 2t# (Power Rule)
#x=tsin(t)#
#dx/dt = sin(t) + tcos(t)# (Product Rule)
Placing these into our formula for the derivative of parametric equations, we have:
#dy/dx = (dy/dt)/(dx/dt) = (2t)/(sin(t)+tcos(t))#