Question
Can someone explain the method of implicit differentiation to me.
I know that we differentiation both sides of the equation with respect to x (I don't understand what they mean by with respect to x). And then y is a function of x...I don't understand what that means.
For example,
Find y'' if x^4+y^4 = 16
Basically we need to differentiate both sides..as far as I know..
so ..(for y')
4x^3+4y^3 = 0
BUT..
in the textbook it's
4x^3+4y^3y' = 0
Where does the y' come from?
I know that we differentiation both sides of the equation with respect to x (I don't understand what they mean by with respect to x). And then y is a function of x...I don't understand what that means.
For example,
Find y'' if x^4+y^4 = 16
Basically we need to differentiate both sides..as far as I know..
so ..(for y')
4x^3+4y^3 = 0
BUT..
in the textbook it's
4x^3+4y^3y' = 0
Where does the y' come from?