Answer:

Hence, the slope ,

Explanation:
We need to find the slope, i.e.
.
and all the functions are in terms of
.
So this looks like a job for the 'chain rule', we can write:
Given the functions

and

we can differentiate them both w.r.t to

first we'll derivate Eq(B) to find dx/dt

we can also rearrange Eq(B) to find x in terms of t ,
. This is done so that
is only in terms of t.

we can find the value of this derivative using t = 3, and plug that value in Eq(A).

now let's differentiate Eq(C) to find dy/dt

rearrange Eq(C), to find y in terms of t, that is
. This is done so that we can replace y in
to make only in terms of t

we can find the value of this derivative using t = 3, and plug that value in Eq(A).

Finally we can plug all of our values in Eq(A)
but remember when plugging in the values that
is being multiplied with
and NOT
, so we have to use the reciprocal!

our slope is equal to
