Question

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

Answer 1

`(dy)/(dx)=2e^(2t^2-2)`

Explanation:

In parametric form of function where `f(t)=(g(t),h(t))`

`(dy)/(dx)=((dh)/(dt))/((dg)/(dt))`

as such derivative of given function is

`(d/dt(e^(2t^2-2)))/(d/(dt)(t^2+1)`

= `(e^(2t^2-2)xx4t)/(2t)`

= `2e^(2t^2-2)`