Question

Fill in the Blank.

If 3x²y + 3xy² = 0, then `(dy)/(dx)` = ______.

Answer 1

If 3x²y + 3xy² = 0, then `(dy)/(dx)` = −1.

Explanation:

3x²y + 3xy² = 0

Dividing both sides by 3xy, we get

`(3x^2y)/(3xy) + (3xy^2)/(3xy) = 0/(3xy)`

x + y = 0

Differentiating both sides w.r.t. x, we get

`d/(dx)  (x) + d/(dy)  (y) = d/(dx)  (0)`

∴ The derivative of x with respect to x is 1

`1 + (dy)/(dx) = 0`

∴ `(dy)/(dx) = - 1`