1. ## Polynomial Derivative

I've answered this question but I can't get e right (I assume j'(m)*k'(m)=l'(m), but I can't make it work).

$\displaystyle GIVEN: j(m)=2m^2+m-6, k(m)=m^3+4$

a. Calculate j'(m) and k'(m)

$\displaystyle j'(m)=4m+1, k'(m)=3m^2$

b. l(m)=j(m)*k(m), work out a polynomial expression for l(m).

$\displaystyle l(m)=2m^5+m^4-6m^3+8m^2+4m-24$

c. Calculate l'(m)

$\displaystyle l'(m)=10m^4+4m^3-18m^2+16m+4$

d. Calculate j'(m)*k'(m)

$\displaystyle 12m^2+3m$

...

I see no corrilation, that's why I need help. I think I didn't work out a polynomial properly? If someone could explain that'd be great.

2. You aren't making a mistake. (Well, except that it should be $\displaystyle 12m^3+3m^2$.) The point of the assignment appears to be to make you recognize that the product of the derivatives is NOT equal to the derivative of the product.

3. i am not sure but perhaps 3m(4m+1) may be one of the zeros of the polynomial l'(m).

4. Originally Posted by drumist
You aren't making a mistake. (Well, except that it should be $\displaystyle 12m^3+3m^2$.) The point of the assignment appears to be to make you recognize that the product of the derivatives is NOT equal to the derivative of the product.
Thanks, so a polynomial can have a power higher than four? That was my other concern.

5. Originally Posted by RAz
I've answered this question but I can't get e right (I assume j'(m)*k'(m)=l'(m), but I can't make it work).
No, j'(m)*k'(m) is not the same as l'(m)

$\displaystyle GIVEN: j(m)=2m^2+m-6, k(m)=m^3+4$

a. Calculate j'(m) and k'(m)

$\displaystyle j'(m)=4m+1, k'(m)=3m^2$

b. l(m)=j(m)*k(m), work out a polynomial expression for l(m).

$\displaystyle l(m)=2m^5+m^4-6m^3+8m^2+4m-24$

c. Calculate l'(m)

$\displaystyle l'(m)=10m^4+4m^3-18m^2+16m+4$

d. Calculate j'(m)*k'(m)

$\displaystyle 12m^2+3m$
No, you've dropped a power of m. You multiplied by 3m, not $\displaystyle 3m^2$.