# Find The Derivative

1. Feb 25, 2010

### polak333

1. The problem statement, all variables and given/known data

y =x4(2x-5)6

2. Relevant equations

Product Rule & Power of a Function Rule

3. The attempt at a solution

y = x4(2x-5)6
y' = 4(x)3(1)(2x-5)6 + x4(6)(2x-5)5(2)
y' = 4x3(2x-5)6 + 12x4(2x-5)5

The answer is:
20x3(2x-5)5(x-1)

No idea where they get the 20x3 or the (x-1). If I were to factor my answer, I still wouldn't get that, I think.

2. Feb 25, 2010

### Staff: Mentor

Your answer is correct but unfactored. Pull the greatest common factor (GCF) out of the two separate terms, as shown below.
4x3(2x - 5)6 + 12x4(2x - 5)5
= 4x3(2x - 5)5(2x - 5 + 3x)
= 4x3(2x - 5)5(5x - 5)
= 5*4x3(2x - 5)5(x - 1)
= 20x3(2x - 5)5(x - 1)

3. Feb 25, 2010

### polak333

Thanks!

Can you help me out with one more?

y = (1-x2)3 (6+2x)-3
y' = 3 (1-x2)2 (-2x)(6+2x)-3 + (1-x2)3(-3)(6+2x)-4(2)
y' = -6x (1-x2)2(6+2x)-3 - 6(1-x2)3(6+2x)-4

Not exactly sure what to do with this.

I could possibly:
y' = -6 (1-x2)(6+2x)-3[x-(1-x2)(6+2x)-1]

or should I put the (6+2x) on the bottom:
y' = -6x(1-x2)2 - 6(1-x2)3
......---------- .. ----------
........(6+2x)3 ..... (6+2x)4

The answer is:

-6(1-x2)2(x2+6x+1)
-------------------
........(6+2x)4

4. Feb 25, 2010

### Staff: Mentor

The common factor is 6(1 - x2)2(6 + 2x)-4. Pull that out and then combine what's left.

5. Feb 25, 2010

### polak333

y = (1-x2)3 (6+2x)-3
y' = 3 (1-x2)2 (-2x)(6+2x)-3 + (1-x2)3(-3)(6+2x)-4(2)
y' = -6x (1-x2)2(6+2x)-3 - 6(1-x2)3(6+2x)-4

That's kind of the problem. I'm not sure how to take out < -6(1 - x2)2(6 + 2x)-4 >.

In the 3rd line, there is a (6+2x)-3, how do you take out (6+2x)-4? Does the power become a positive, and therefore: (6+2x)1 which is just (6+2x)?

6. Feb 25, 2010

### polak333

Nevermind. I got it.

Thanks for the help!

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