Differentiation of a Quotient check

[DBeckett91]

Homework Statement

S = (8x^2 - 7x + 125)/(8x+7)

Where the value of x is unknown

The Attempt at a Solution

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

v = 8x + 7 dv/dx = 8

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

= (8x+7*16x-7 - 8x^2-7x+125*8)/(8x+7)^2

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

= (128x^2 + 56x - 49) - (64x^2 - 56x + 1000)/(8x+7)^2

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


This rule I'm not very comfortable or confident with so if I have gone wrong anywhere in my equations any help would be much appreciated

 

[HallsofIvy]

Homework Statement

S = (8x^2 - 7x + 125)/(8x+7)

Where the value of x is unknown

The Attempt at a Solution

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

v = 8x + 7 dv/dx = 8

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

= (8x+7*16x-7 - 8x^2-7x+125*8)/(8x+7)^2

You would do better to use parentheses:
[(8x+7)(16x- 7)- (8x^2- 7+ 125)(8)]/(8x+ 7)^2

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

and here you mean [(128x^2 - 56x + 112x - 49) - (64x^2 - 56x + 1000)]/(8x+7)^2

= (128x^2 + 56x - 49) - (64x^2 - 56x + 1000)/(8x+7)^2

The only difference between this and the previous line is that the "112x" is missing. What happened to it?

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


This rule I'm not very comfortable or confident with so if I have gone wrong anywhere in my equations any help would be much appreciated

 

[DBeckett91]

You would do better to use parentheses:
[(8x+7)(16x- 7)- (8x^2- 7+ 125)(8)]/(8x+ 7)^2


and here you mean [(128x^2 - 56x + 112x - 49) - (64x^2 - 56x + 1000)]/(8x+7)^2


The only difference between this and the previous line is that the "112x" is missing. What happened to it?

In the above line there is -56x and +112x so all I did was 112x-56x to gain +56x, it was just some simplification of the equation so I had fewer numbers to work with later on

 

[HallsofIvy]

Oh, I see. Yes, that is the correct answer.