Derivatives have a wide range of applications in engineering, sciences, social sciences, economics and other applications. In this blog, we discuss Derivative as a Rate Measure. Visit Class 12 Differential Calculus, for more resources.
This topic is slightly application oriented, hence students tend to find it a little difficult. However, this post will cover all the topics and formulas that you would need to know along with problems.
dy/dx represents the Rate of change of your w.r.t x. If y increases, dy/dx is positive and if y decreases, dy/ dx is negative
Try this question!
A ladder 5 m long rests against a vertical wall. If the top of the ladder slides downward at the rate of 10 cm/sec. find the rate at which the angle between the floor and the ladder is decreasing when the lower end of the ladder is 2 m away from the wall.
How about this problem?
Find the coordinates of a point on the ellipse where the ordinate decreases at the same rate at which the abscissa increases.
Try this question on Rate Measure!
Find the rate of change of volume of a sphere with respect to its surface area when the radius is 2 cm.
What is a approximation?
When there is a small change in x, there arises a small change in y, this is called the differential of y. The formula to calculate the Differential is illustrated here.
