Question

Let y = f(x) be a function. If the change in one quantity 'y’ varies with another quantity x, then which of the following denote the rate of change of y with respect to x.

Options

• `(dx)/(dy) = f(x)`

• `(dx)/(dy) = f^1(x)`

• `(dy)/(dx) = f^1(x)`

• None of these

Answer 1

`(dy)/(dx) = f^1(x)`

Explanation:

Rate of change of quantities: Let y = f(x) be a function. If the change in one quantity 'y varies with another quantity 'x’, then `(dy)/(dx) = f^1(x)` denotes the rate of change of 'y’ with respect to `x`.

At `x = x_0, [(dy)/(dx)]_(x = x_0)` or `f^'(x)` represents the rate of change of y w.r.t x at `x  = x_0`.