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How to Prepare for Applications of Derivatives-Class 12 Mathematics

Updated: Sep 10

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.

problem on rate measure

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.


Find the coordinates of a point on the ellipse where the ordinate decreases at the same rate as 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.


rate of change question

rate of change solution slide 1

rate of change solution slide 2

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.


Differential


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