Question

How do you differentiate `y=((2x)/(x-1))((3x+4)/(5x^2-7))`?

Answer 1

`dy/dx = (2x)/(x -1)(3x +4)/(5x^2 - 7)(1/x - 1/(x - 1) + 3/(3x + 4) - (10x)/(5x^2 - 7))`

Explanation:

I would use logarithmic differentiation.

Taking the natural logarithm of both sides, we get:

`lny = ln((2x)/(x - 1))((3x +4)/(5x^2 - 7))`

`lny = ln(2x) - ln(x- 1) + ln(3x +4) - ln(5x^2 - 7)`

Now differentiate.

`1/y(dy/dx) = 1/x - 1/(x- 1) + 3/(3x + 4) - (10x)/(5x^2 - 7)`

`dy/dx = y(1/x -1/(x- 1) + 3/(3x + 4) - (10x)/(5x^2 - 7))`

`dy/dx = (2x)/(x -1)(3x +4)/(5x^2 - 7)(1/x - 1/(x - 1) + 3/(3x + 4) - (10x)/(5x^2 - 7))`

Hopefully this helps!