The Chain Rule is a formula for computing the derivative of the composition of two or more functions. For instance, if f and g are functions, then the chain rule expresses the derivative of their composition.
The Chain Rule Formula is as follows –
dy/dx = dy/du * du/dx
1. Direct Proportion : Two quantities are said to be directly proportional. if on the increase (or decrease) of the one, the other increases (or decreases) to the same extent.
Ex. 1. Cost is directly proportional to the number of articles.(More Articles, More Cost)
Ex. 2. Work done is directly proportional to the number of men working on it. (More Men, More Work)
2. Indirect Proportion : Two quantities are said to be indirectly proportional, if on the increase of the one, the other decreases to the same extent and vice-versa.
Ex. 1. The time taken by a car in covering a certain distance is inversely proportional to the speed of the car. (More speed, Less is the time taken to cover a distance )
Ex. 2. Time taken to finish a work is inversely proportional to the number of persons working at it.(More persons, Less is the time taken to finish a job)
Remark : In solving questions by chain rule, we compare every item with the term to be found out.