Question

I need help

Answer 1

finding the derivative x^3+3x^2y+y^3=8

Answer 2

finding the derivative x^3+3x^2y+y^3=8

Answer 3

Finding the derivative WRT (with respect to) x? Hmm we can't solve for y explicitly before we differentiate. So we'll have to differentiate implicitly.
Are you familiar with how to do that? :)
We'll have to do some fancy stuff with the middle and last term.

Answer 4

No I am not familiar

Answer 5

When you differentiate implicitly, differentiate as you would normally, however whenever you take the derivative of y, write dy/dx. Give me a minute and I'll write an example for you.

Answer 6

I have four answers to choose from A.) -x^2+2xy/x^2+y^2
B.) x^2+3xy/x^2+y^2
C.) x^2+2xy/x^2+y^2
D.) -x^2+3xy/x^2+y^2

Answer 7

Example:

3x² - y³ = x²y + 5

Now you differentiate each term with respect to x. Thus whenever taking the derivative of y, multiply by dy/dx. Thus

6x - 2y(dy/dx) = 2xy + x²(dy/dx)

6x - 2xy = x²(dy/dx) + 2y(dy/dx)

6x - 2xy = (dy/dx)(x² + 2y)

∴ dy/dx = (6x - 2xy)/(x² + 2y)

Now you try it your self.

Answer 8

Let me know if there is any part of my example you need me to clarify.