Differentiation: Product rule and composite rule

[imy786]

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

 

[Fredrik]

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).

 

[Mark44]

What both of you are referring to as the "composition" rule, most books that I've seen call the chain rule.

 

[Fredrik]

Hm, for some reason I didn't even realize that I was just repeating what he said in a slightly different way. 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.