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# Differentiation watch

1. how is the differential of 1+tan2(4x)

8*tan(4x)*sec2(4x)
2. Because the differential of Tan is Sec^2
3. (Original post by jsmith6131)
how is the differential of 1+tan2(4x)

8*tan(4x)*sec2(4x)
Term-by-term differentiation with the chain rule on the second term twice. If it's not immediately clear, let and so .

Note that , the RHS of which should be more straightforward to evaluate.
4. Note that

Might be easier to differentiate that way, well it would be for me
5. so
4*sec(4x)*sec(4x)*tan(x)
where do I get
8... from?
6. oh
got it
u2 goes to 2u
sec4x goes to 4sec(4x)tan(4x)
2*sec(4x)*sec(4x)*tan(4x)

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Updated: November 27, 2011
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