How do you differentiate the following parametric equation: # x(t)=te^t , y(t)=e^t #?

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Answer 1 · 2015-12-08T06:50:07

#dy/dx = 1/(t+1)#

#dy/dx = (dy/dt)/(dx/dt) = (y'(t))/(x'(t))#

Applying that here, we use the product rule as well as that #d/dxe^x = e^x# to find

#x'(t) = d/dtte^t = te^t+e^t = e^t(t+1)#

and

#y'(t) = d/dte^t = e^t#

Thus

#dy/dx = e^t/(e^t(t+1)) = 1/(t+1)#