Published: 05 Aug 2019

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.

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