Question

Write the derivative as rate measure using example

Answer 1

If  y = f(x),    Then

dy/dx = f'(x)           (read as Derivative of y w.r.t. x)

⇒ Derivative provides us rate of change of ONE variable w.r.t the other variable.

Example:  Suppose that the sun is rising. It is passing directly over a building. The height of the building is 100 feet. Let θ be the angle of elevation of the sun. Also let x be the length of the shadow of the building. Find the rate at which x is changing with respect to θ.

Also find the answer for θ = 45°.

Answer 2

Answer:

Step-by-step explanation:

If a quantity y depends on and varies with a quantity x then the rate of change of y with respect to x is

$\frac{dy}{dx}$

For example ,the rate of change of pressure p with respect to h is

$\frac{dp}{dh}$

A rate of change with respect to time

is usually called as 'rate of change' the 'with respect to time' being assumed.

For example,the rate of change of current i is

$\frac{di}{dt}$