Differentiation: How to use the chain rule

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