Differentiation: How to use the chain rule

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If y is a function of u, which itself is a function of x, then 

dy/dx=(dy/du) x (du/dx)

Differentiate the outer function and multiply by the derivative of the inner function.  

To illustrate this rule, look at the example below:

y=(2x+3)10

in which y=u10 and u=2x+3

Now,

dy/du=10u9=10(2x+3)9

du/dx=2

The chain rule then gives

dy/dx=(dy/du) x (du/dx) = 10(2x+3)9(2) = 20(2x+3)9

 
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