# another question

• Dec 13th 2008, 06:40 PM
mech.engineer.major
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.
• Dec 13th 2008, 06:44 PM
mr fantastic
Quote:

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.

• Dec 13th 2008, 07:20 PM
mech.engineer.major
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.
• Dec 13th 2008, 07:48 PM
mr fantastic
Quote:

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.