Differentiation: Product rule and composite rule

  • Thread starter imy786
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  • #1
imy786
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Homework Statement




Use differentiation to verify that the following integrals are correct (where a is not = 0 is a constant and c is an arbitrary constant

(a) integrate xsinax dx= ( −x/a ) (cosax) +(1/a2) sinax+c

(b) integrate tanax dx=(−1/a) ln(cosax)+c

Homework Equations



Composite rule dy/dx = (dy/du) (du/dx)


The Attempt at a Solution



Im not getting the right solution after diffrenting.

attached are my solutions
 

Answers and Replies

  • #2
Fredrik
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I don't see an attachment. For the first problem, you also need the product rule. For the second one, you need to use the chain rule twice.

(Edited after Mark44's reply below).
 
Last edited:
  • #3
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What both of you are referring to as the "composition" rule, most books that I've seen call the chain rule.
 
  • #4
Fredrik
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Hm, for some reason I didn't even realize that I was just repeating what he said in a slightly different way. :rolleyes: Yes, the "chain rule" is what I'd normally call it. I don't think I've seen it called anything else in a book.
 

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