Why is the constant 5 instead of 5y in F(y) derivative?

[jimen113]

Homework Statement

RE: F(y)= (1/y$$\hat{}2$$ - 3/y$$\hat{}4$$)(y+5y)
the answer is: F=5+14/y$$\hat{}2$$+9/y$$\check{}4$$

The Attempt at a Solution

F(y)= (f*g)$$\acute{}$$
f$$\acute{}$$*g)+(f*g$$\acute{}$$)

(-2y$$\hat{}-3$$+12y$$\hat{}-5$$)*(y+5y$$\hat{}3$$)+(y$$\hat{}-3$$-3y$$\hat{}-4$$)*(1+15y$$\hat{}2$$)
so, I get (14/y$$\hat{}2$$ +9/y$$\hat{}4$$)+5y,
which is very close to the answer in the book, except that instead of 5y they have the answer as just (14/y$$\hat{}2$$ +9/y$$\hat{}4$$)+5
??

 

[sutupidmath]

I cannot clearly read what you did, but you first need to apply the product rule tha is
let $$f(y)=y^{-2}-3y^{-4}, \ \ and \ \ \ g(y)=6y$$ so

$$F(y)=f(y)*g(y)=>F'(y)=f'(y)*g(y)+g'(y)*f(y)$$

or you could merely foil everyghing out and you would end up with:

$$F(y)=6y^{-1}-18y^{-3}$$ and then take the derivative of this one.


However i think that you originally gave us the wrong function, for there is no way you can get the answer you provided us. check it again, for i won't do it for you. Because by just integrating the result you gave us, one cannot get the function you provided.