## Question

###### What is the derivative of #f(t) = (e^(t^2-1)-t, 2t^2-4t ) #?

What is the derivative of #f(t) = (e^(t^2-1)-t, 2t^2-4t ) #?

## Answers

#(dy)/(dx)=(4t-4)/(2te^(t^2-1)-1)# ## Explanation:

Derivative of a parametric function

#f(t)=(x(t),y(t))# is given by#(dy)/(dx)=((dy)/(dt))/((dx)/(dt))#

As#y(t)=2t^2-4t# ,#(dy)/(dt)=4t-4# and as

#x(t)=e^(t^2-1)-t# ,,#(dx)/(dt)=e^(t^2-1)xx2t-1=2te^(t^2-1)-1#

#(dy)/(dx)=(4t-4)/(2te^(t^2-1)-1)#

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