Tuesday, January 21, 2014

High School Math Solutions – Derivative Calculator, the Chain Rule

In the previous posts we covered the basic derivative rules, trigonometric functions, logarithms and exponents (click here).  But we are still missing the most important rule dealing with compound functions, the chain rule.

Why is it so important?  Because most of the functions you will have to derive, and later integrate, are most likely compound.  For example sin(2x) is the composition of f(x)=sin(x) and g(x)=2x or √(x²-3x) is the composition of f(x)=√x and g(x)= x²-3x

The chain rule formula is as follows:  (f(g(x)))’=f’(g(x)) *g’(x)
That is, the derivative of the composition of two functions equals the derivative of the outer function times the derivative of the inner function

Let’s start with an example to see how it works (click here):

Here’s a more complex example involving multiple applications of the chain rule (click here):

With the chain rule we put it all together; you should be able to derive almost any function.  There are some advanced topics to cover including inverse trig functions, implicit differentiation, higher order derivatives, and partial derivatives, but that’s for later.

Until next time,


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  3. I'm trying to understand the notation the calculator uses, in the symbolab tutorials and on this page it uses (f(g(x)))’=f’(g(x)) *g’(x) style of notation, but the calculator uses f and u instead. I'm having a hard time interpreting how to compute chains when the system I use to check my work is using a different notation. I've noticed that the u=g between the two systems but why does the calculator use a different notation than what is taught (even in your own tutorials)?

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