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

1 Answer
Nov 1, 2017

Answer:

#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!