calculus question?

Question

If y = (x−4)/(12 x−4)

find dy/dx

show all working out
thanks

Answer 1

you name (x-4) =u, (12x-4)=v

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

du/dx =1, dv/dx =12

so dy/dx= (12x-4)-12(x-4) / (12x-4)^2

dy/dx= 44/(12x-4)^2

Answer 2

If (x-4) = A and (12x-4) = B, you use the equation
(A'B -AB') / B^2, where ' means the derivative of that fraction
A' = 1, B' = 12
So using the quotient rule(listed above), you get
[1*(12x - 4) - 12(x-4)] / [(12x-4)^2] = dy/dx
(12x - 4 -12x +48) / (12x-4)^2 = dy/dx
44 / (12x-4)^2 = dy/dx
You can pull a multiple of 4 out of the denominator, but make sure you take the square root of it before dividing the numberator.
44 / [2*(3x-1)^2] = dy/dx
22 / (3x-1)^2 = dy/dx

Answer 3

General approach:
y = (1/4)(x-4 )/(3 x−1)
y' = (1/4)(3x-1-3x-12)/(3 x−1)^2 = 11/[4(3 x−1)^2]

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A different approach:
y
= (1/4)(x-4 )/(3 x−1)
= (1/12)(3x-1 - 11)/(3 x−1)
= 1/12 - (11/12)/(3 x−1)

y' =(11/12)*3/(3 x−1)^2 = 11/[4(3 x−1)^2]
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Answer 4

y=(x-4)/4(3x-1)
=(3x-12)/12(3x-1)
=(1/12)(1-11/(3x-1))

dy/dx=(1/12)(33/(3x-1)^2 )
=1/4(3x-1)^2

Answer 5

u=(x-4) v=(12x-4)
dy/dx=udv+vdu
(x-4)(12)+(12x-4)(1)
12x-48+12x-4
24x-52

Answer 6

d/dx(f/g) = (gf'-fg')/g^2
dy/dx= 44/(12x-4)^2

Answer 7

If y = f(x)/g(x), then

y' = [f'(x)*g(x) - f(x)*g'(x)]/[g(x)^2]