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Question
Fill in the Blank.
If 3x2y + 3xy2 = 0, then `(dy)/(dx)` = ______.
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Solution
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`
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