Question

Differentiate x^2+5x-6/4x^2-x+3

Answer 1

Answer:

$\displaystyle\frac{-3(7x^2-18x-3)}{(4x^2-x+3)^2}$

Step-by-step explanation:

Put u = x² + 5x - 6  and  v = 4x² - x + 3

Then du/dx = 2x + 5   and   dv/dx = 8x - 1.

The required derivative is:

d(u/v)/dx

= ( v du/dx - u dv/dx ) / v²

= ( ( 2x + 5 ) ( 4x² - x + 3 ) - ( 8x - 1 ) ( x² + 5x - 6 ) )  /  v²

= ( ( 8x³ + 18x² + x + 15 ) - ( 8x³ + 39x² - 53x + 6 ) ) / v²

= ( -21x² + 54x + 9 ) / v²

= -3 ( 7x² - 18x - 3 ) / ( 4x² - x + 3 )²

Answer 2

Answer:

4x2-x+3 (2x+5) - x2+5x-6 (8x-1)/ (4x2-x+3)