R D Sharma Solutions for Chapter: Derivative as a Rate Measurer, Exercise 1: EXERCISE

Find the rate of change of the volume of a sphere with respect to its diameter.

Find the rate of change of the volume of a sphere with respect to its surface area when the radius is $2\mathrm{cm}.$

Find the rate of change of the area of a circular disc with respect to its circumference when the radius is$3 \mathrm{cm}.$

Find the rate of change of the volume of a cone with respect to the radius of its base ?

Find the rate of change of the area of a circle with respect to its radius $r$ when $r=5 \mathrm{cm}$.

Find the rate of change of the volume of a ball with respect to its radius $r$. How fast is the volume changing with respect to the radius when the radius is $2 \mathrm{cm}$?

The total cost $C\left(x\right)$ associated with the production of $x$ units of an item is given by $C\left(x\right) = 0.007x^3- 0.003x^2+ 15x+ 4000$. Find the marginal cost when $17$ units are produced ?

The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (Marginal revenue). If the total revenue (in rupees) recieved from the sale of $x$ units of a product is given by $R\left(x\right)=3x^2+36x+5$, find the marginal revenue, when $x=5$, and write which value does the question indicate ?