Differentiation question?

Question

Hi. I would like to find out the answer to this question.

If

y = (4*x+1) / (3*x-4)

in words...

y equals 4x plus 1 divided by 3x minus 4.....

then what is dy/dx ??

Thanks for any help received. It is very much appreciated.

Answer 1

y = (4x + 1) / (3x - 4)

this is a quotient so we use the quotient rule

y = u/v

u = 4x + 1 so u ' = 4

v = 3x - 4 so v ' = 3

dy/dx = (v u' - u v ' ) / v²

= ((3x - 4)(4) - (4x + 1)(3)) / (3x - 4)²

= (12x - 16 - 12x - 3) / (3x - 4)²

= -19 / (3x - 4)²

Answer 2

y = (4*x+1) / (3*x-4)

dy/dx = [(3)(4x + 1) - (3x - 4)(4)]/(3x - 4)^2

dy/dx = [12x + 3 - 12x + 16]/(3x - 4)^2

dy/dx = (19)/(3x - 4)^2       ANSWER

Hope this helps.

teddy boy