1. ## another question

I have another question if someone wouldn't mind helping me.

how would you differentiate:

y = ((x^2+4)^2) * ((2x^3-1)^3)

My first thought was that it involved two separate Chain Rules within a Product Rule. This seemed to work until I got a little stuck on how to simplify.

2. Originally Posted by mech.engineer.major
I have another question if someone wouldn't mind helping me.

how would you differentiate:

y = ((x^2+4)^2) * ((2x^3-1)^3)

My first thought was that it involved two separate Chain Rules within a Product Rule. This seemed to work until I got a little stuck on how to simplify.

3. this is how far I got:

y= ((x^2+4)^2) * ((2x^3-1)^3)

y= (((x^2+4)^2) * (3(2x^3-1)^2)*(6x^2)) + (((2x^3-1)^3) * (2(x^2+4)2x)

y= (((x^2+4)^2) * (18x^2(2x^3-1)^2)) + (((2x^3-1)^3) * (4x^3+16x))

y= ?

As far as I can tell I performed the Product Rule with the Chain Rules correctly but I'm not sure how it wraps up.

4. Originally Posted by mech.engineer.major
this is how far I got:

y= ((x^2+4)^2) * ((2x^3-1)^3)

dy/dx = (((x^2+4)^2) * (3(2x^3-1)^2)*(6x^2)) + (((2x^3-1)^3) * (2(x^2+4)2x)

dy/dx = (((x^2+4)^2) * (18x^2(2x^3-1)^2)) + (((2x^3-1)^3) * (4x^3+16x))

dy/dx = ?

As far as I can tell I performed the Product Rule with the Chain Rules correctly but I'm not sure how it wraps up.
Now you factorise the expression by taking out the common factor, which appears to be $2x (2x^3 - 1)^2 (x^2 + 4)$ ....