Determine $(f\circ g)'(x)$ if $f(x)=2x$ and $g(x)=3x$.

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Lesson Parent: 
The Chain Rule
Problem: 

Determine $(f\circ g)'(x)$ if $f(x)=2x$ and $g(x)=3x$.

Answer: 

$(f\circ g)'(x)=6$

SAMPLE SOLUTION

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Solution: 

We have already determined that <Sign in to see all the formulas>. From our differentiation formulas we see that <Sign in to see all the formulas>.

Let's apply the Chain Rule to find <Sign in to see all the formulas>. We first find <Sign in to see all the formulas> and <Sign in to see all the formulas>. This problem is easy because there is no $x$ in $f'(x)$ <Sign in to see all the formulas>. Since <Sign in to see all the formulas> we see that <Sign in to see all the formulas>.

Note that we found <Sign in to see all the formulas> two different ways. The first by directly determining <Sign in to see all the formulas> and then calculating its derivative. The second method was by determining $f'(x)$ and $g'(x)$ and then using the Chain Rule to determine <Sign in to see all the formulas>. Both methods came up with the same answer as they should.