In our book of co-ordinate geometry, we have already learnt that the Cartesian equation of the conics can also be given in the parametric form. For example the parabola *y*^{2} = 4*ax*; the parametric from is given by *y* = 2*at* and *x* = *at*^{2}. Therefore having established that a function '*y*' of '*x*' can be represented by the parametric equations as well. Lets say *x* = *g*(*t*) and *y* = *h*(*t*) are the parametric equations of *y* = *f*(*x*).

Now, let us assume that these functions are differentiable and the inverse of the functions *x* = *g*(*t*) is given by *t* = *G*(*x*).

*f*(*x*) = *y* = *h*(*t*) and *t* = *G*(*x*)

∴ *f*(*x*) = *y* = *h*(*G*(*x*))

Differentiating w.r.t *x*; we get

Also, Since *x* = *g*(*t*) and *t* = *G*(*x*) are the inverse functions of each other, Therefore

Substituting this ...

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