Question
Thu April 09, 2015 By: Yatish Sekaran

What is chain rule in differentation?is there any formulae associated with it?
Explain it with an example, please
for eg., What is chain rule in differentation, Question no 89552, Mathematics

Expert Reply
satyajit samal
Fri April 10, 2015
Chain rule is just a method to find derivative of a function which is a composition of two or more functions.
For example:
1. To find the derivative of cos(sin x) with respect to 'x', first we differentiate cos(sin x) with respect to sin x.
Derivative of cos (sin x) with respect to sin x is -sin (sin x).
Now, derivative of sin x with respect to 'x' is cos x.
Hence, derivative of cos (sin x) with respect to 'x' is -sin (sin x) * cos x.
2. To find the derivative of cos2x with respect to 'x', first we find derivative of cos2x with respect to cos x.
Derivative of cos2x with respect to cos x is 2 cos x.
Now, derivative of cos x with respect to 'x' is -sin x.
Hence derivative of cos2x with respect to 'x' is (2 cos x * -sin x).
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