Question

a- what is the difference between the derivative of X^n and y^n (explain the followings: how many terms each derivative has, which one has more terms, and what is the extra term)

b- Write summary of the steps to take (guidelines) for implicit differentiation, to find y'

Answer 1

a. We have given that so we take derivative with respect to x then what we get is

by the simple derivative rule and if we have the function as now we take derivative with respect to x then what we get is since y is the function of x. So we have seen that in first case it is direct derivative while in the other case it is in general the chain rule we applued and get it.

b. If we assume that

Then by taking derivative with respect to x then

And if we say

Then by taking derivative with respect to x

Then

And hence

So we get that y'=0