Question

consider the curve given by xy^2-x^3y=6
Show that dy/dx=3x^2y-y^2/2xy-x^3

Answer 1

Use implicit derivation. Do you know how?

Answer 2

No, sadly.

Answer 3

You have to suppose that y = y(x) and you don't know, explicitly, its derivative.
Hence, you differentiate as you always did, thus:

xy^2-x^3y=6 <=> y^2 + x*2y*(dy/dx) + [rest]

Is it clear?

Answer 4

I don't understand the second part? y^2 + x*2y*(dy/dx) + [rest]

Answer 5

If you had, instead, this function to differentiate this function :

x^(3n)

How would you do?

Answer 6

I honestly have no idea. I missed this lesson during class.

Answer 7

How can you miss the basics of derivative of a function like x^n and now you are asked to do implicit differentiation... I'm not a fool, sorry.

Answer 8

x^n= nx^n-1