The Chain Rule
How do we differentiate F(x)=Tan(2x-4)? This function is the composite FoG of two functions F (u)=Tan u and u=2x-4 that we know how to differentiate. The Chain rule states that the correct answer to F(x) is derived by multiplying the derivatives of F and G.
To begin, it is best to start by breaking the problem into its F (u) or
F form and its u or G forms.
Now that we’ve done that, we should take the derivatives of each form.
F ‘(u)=F ‘=Sec^2(u)
(Notice the u in the parenthesis is NOT derived)
u ‘=G ‘= 2
Using the Chain Rule, we know that we must now multiply F ‘ and G ‘.
We cannot leave u in our final answer, so knowing that u=2x-4, we can write the final answer as:
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