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Question
The rate of change of demand (x) of a commodity with respect to its price (y), if y = 20 + 15x + x3.
Solution: Let y = 20 + 15x + x3
Diff. w.r.to x, we get
`("d"y)/("d"x) = square + square + square`
∴ `("d"y)/("d"x)` = 15 + 3x2
∴ By derivative of the inverse function,
`("d"x)/("d"y) 1/square, ("d"y)/("d"x) ≠ 0`
∴ Rate of change of demand with respect to price = `1/(square + square)`
Solution
Let y = 20 + 15x + x3
Diff. w.r.to x, we get
`("d"y)/("d"x)` = 0 + 15 + 3x2
∴ `("d"y)/("d"x)` = 15 + 3x2
∴ By derivative of the inverse function,
`("d"x)/("d"y) 1/(("d"y)/("d"x)), ("d"y)/("d"x) ≠ 0`
∴ Rate of change of demand with respect to price = `1/(15 + 3x^2)`
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