DERIVATIVES HELP.

3. y= (3x²-4x+4)³ / 2x²-4x+3    I'm going to write this in a slightly different manner to avoid using the Quotient Rule....so we have.....

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

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

Factor

[ (3x^2 - 4x + 4)^2 * (2x^2 - 4x + 3)^(-2)]  *  [ 3(6x - 4)(2x^2 - 4x + 3) - (4x - 4)(3x^2 - 4x + 4) ]  =

[The expression in the second bracket is a little messy to simplify.......I'll use WolframAlpha to help out !!!  ]

[(3x^2 - 5x + 3)^2 * (2x^2 - 4x + 3)^(-2)] * [ 24x^3 - 68x^2 +70x - 20]

  2. y= (4x2+3x-1) sqrt. 5x-7    I'm assuming that this one is multiplication???...if so, we have

y' =  (8x +3)(5x - 7)^(1/2)  + (1/2)(5x -7)^(-1/2)(5)(4x^2 + 3x -1)

Factor

(5x - 7)^(-1/2) [ (8x + 3)(5x - 7) + (5/2)((4x^2 + 3x -1) ] =

(5x - 7)^(-1/2) [ 40x^2 - 41x - 21 + 10x^2 + (15/2)x - 5/2 ]  =

(5x - 7)^(-1/2) [ 50x^2 - (67/2)x - 47/2)

4. y= 2x^2-5x+7 / sqrt. 4x-5

Again, I'll write this as

4. y= (2x^2-5x+7) * (. 4x-5 )^(-1/2)

y' = (4x -5) *(4x - 5)^(-1/2)   - (1/2)(4x - 5)^(-3/2)*(4) * ( 2x^2 - 5x + 7)

(4x - 5)^(1/2) - (4x - 5)^(-3/2)*(2) * (2x^2 - 5x + 7)

Factor

[ (4x - 5)^(-3/2) * [ (4x - 5)^2 - 2(2x^2 - 5x + 7) ]

[(4x - 5)^(-3/2) ] [ 16x^2 - 40x + 25 - 4x^2 + 10x - 14 ]

[(4x - 5)^(-3/2)] [ 12x^2 - 30x + 11]