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
NH
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