Expert: Ahmed Salami - 1/3/2010

Question
Differentiate: y=3x/x^2+1

Answer
Hi Saadiq,
For this kind of expressions we use the quotient rule to find the derivative.
If y = u/v
dy/dx = [v.du/dx - u.dv/dx] / v²
Now,
y = 3x/(x² + 1)
Take u = 3x and v = x² + 1
du/dx = 3 and dv/dx = 2x
dy/dx = [(x² + 1)(3) - (3x)(2x)] / (x² + 1)²
     = [(3x² + 3) - (6x²)] / (x² + 1)²
     = (3 - 3x²) / (x² + 1)²
     = 3(1 - x²)/(x² + 1)²
     = 3(1 + x)(1 - x)/(x² + 1)²

Regards