Have I got this correct? (Quotient rule)

[DBeckett91]

Thanks in advanced for help on this, if I have gone wrong anywhere along the way please don't hesitate to point out my mistake(s).

Homework Statement

Differatiate each question with respect to the variable.

s =(Ax^2-kx+w)/Ax+k

Homework Equations

Quotient rule: ds/dx=((v*du/dx)-(u*dv/dx))/v^2

The Attempt at a Solution

s = u/v

u = 8x^2-7x+125
v = 8x+7

du/dx = 8x^2-7x+125
= 16x-7

dv/dx = 8x+7
= 8

ds/dx=((v*du/dx)-(u*dv/dx))/v^2

ds/dx=((8x+7*16x-7)-(8x+7*8))/8x+7^2
ds/dx=((128x^2-56x+112x-49)-(64x^2-56x+1000))/8x+7^2
ds/dx=((128x^2-56x-49)-(64x^2-56x+1000)/8x+7^2
ds/dx=(64x^2+951)/8x+7^2

 

[Mark44]

Thanks in advanced for help on this, if I have gone wrong anywhere along the way please don't hesitate to point out my mistake(s).

Homework Statement

Differatiate each question with respect to the variable.

s =(Ax^2-kx+w)/Ax+k

Is this the function you need to differentiate? Your work below has has A = 8 and k = 7.

Also, you need parentheses around the entire denominator, like this:
s =(Ax^2-kx+w)/(Ax+k)

Homework Equations

Quotient rule: ds/dx=((v*du/dx)-(u*dv/dx))/v^2

The Attempt at a Solution

s = u/v

u = 8x^2-7x+125
v = 8x+7

du/dx = 8x^2-7x+125
= 16x-7

dv/dx = 8x+7
= 8

ds/dx=((v*du/dx)-(u*dv/dx))/v^2

ds/dx=((8x+7*16x-7)-(8x+7*8))/8x+7^2
ds/dx=((128x^2-56x+112x-49)-(64x^2-56x+1000))/8x+7^2

Except for missing parentheses around the denominator, the above is fine.

ds/dx=((128x^2-156x-19)-(64x^2-56x+1000)/8x+7^2

How did you get the above? Specifically, how did -56x + 112x turn into -156x, and how did -49 turn into -19?

ds/dx=(64x^2+951)/8x+7^2

 

[DBeckett91]

Sorry that was a typo, the post is now edited to be the numbers I intended. As for the value of A, k and w:
A = 8
k = 7
w = 125

I must have missed that bit also