And explain, don't just tell me the answer because I know it I just don't know how to get it

answers:
Jessica say: henot sure what to say about this

Linda K say: by power rule: 3(3+2x  x^2)^2 then * the derivative of inside of ( ) by chain rule
3(3 +2x x^2)^2 (2 2x)
3(3+2x x^2)^2 *2(1x)
6(1x)(3+2x  x^2)^2 you can factor the quadratic
6(1x)((1 x)(3x))^2
6(1x)^3(3x)^2

Deepak Suwalka say: y = ( 3 + 2x  x² )³
Using power and chain rule we get:
dy/dx = 3(3 + 2x  x²)² × d/dx (3 + 2x  x²)
= 3(2  2x)( 3 + 2x  x² )²

Sqdancefan say: Use the power and chain rules.
.. d(u^3)/dx = 3u^2*(du/dx)
For u = 3 +2x x^2, du/dx = 2 2x and the derivative is
.. 3*(3 +2x x^2)^2*(2 2x)
.. = 6*(1 x)*(3 +2x x^2)^2

Steve A say: Let (3+2xx^2) = u
Derivative u^3 = 3u^2 du
Thus, 3(3+2xx^2)^2(2  2x)
(6  6x)(3 + 2x  x^2)^2

? say: y=(3+2xx²)³
power rule + chain rule
y'=3(3+2xx²)²•(3+2xx²)'
= 3(3+2xx²)²(22x)
= 3(x²2x3)²•2(x1)
= 6(x1)((x3)(x+1))²
= 6(x1)(x+1)²(x3)²

az_lender say: y = (3+2xx^2)^3, call this u^3.
dy/dx = (dy/du)(du/dx)
= (3u^2)(2  4x)
= 3(3+2xx^2)^2 * (24x).
It is not necessary to carry out the multiplication.

J say: (3+2xx^2)^3 = x^6 + 6 x^5  3 x^4  28 x^3 + 9 x^2 + 54 x + 27
now just differentiate term by term

Jim Moor say: Here:

hayharbr say: If it was just x^3, you'd get 3x^2. But you can't just say this derivative is
3(3 + 2x  x^2) ^ 2
When there is more than just x, you have to do the derivative of what's inside the parentheses and multiply by the 3(3 + 2x  x^2) ^ 2
so the final answer is 3(2  2x)(3 + 2x  x^2)^2
It's the chain rule:
let u = 3 + 2x  x^2
and y = u^3
You want dy/dx but can only find dy/du and du/dx
But that's ok because dy/dx = dy/du • du/dx
so since du/dx = 2  2x, and dy/du = 3u^2, dy/dx = (2  2x)(3u^2) and subbing back for u, you get
(2  2x)(3(3 + 2x  x^2)^2)
or 3(2  2x)(3 + 2x  x^2)^2
That's how I learned it anyway.

Kara say: heNot sure what to say about this
