Question

What is the derivative of `f(t) = (t^3-e^(1-t) , tan^2t )`?

Answer 1

`(dy)/(dx)=(3e^2+e^(1-t))/(2tant*sec^2t)`.

Explanation:

`f(t)=(t^3-e^(1-t),tan^2t)` is a parametric function in which both `x` and `y` are function of `t`.

As such `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`.

Here `(dy)/(dt)=3e^2-(-1)*e^(1-t)=3e^2+e^(1-t)` and

`(dx)/(dt)=2tant*sec^2t`

Hence `(dy)/(dx)=(3e^2+e^(1-t))/(2tant*sec^2t)`.