# Math Help - Differentiation

1. ## Differentiation

Hi, I've already proven that dy/dx=1/2{1-(9/[2t^2+1])}

How do I show that dy/dx<1/2??

Thanks a lot!

2. Originally Posted by cyt91
Hi, I've already proven that dy/dx=1/2{1-(9/[2t^2+1])}

How do I show that dy/dx<1/2??

Thanks a lot!
Hi cyt91,

$\frac{dy}{dx}=\frac{1}{2}\left[1-\left(\frac{9}{2t^2+1}\right)\right]=\frac{1}{2}\left[\frac{2t^2+1}{2t^2+1}-\frac{9}{2t^2+1}\right]$

$=\frac{1}{2}\left[\frac{2t^2+1-9}{2t^2+1}\right]$

and as the numerator of the second factor is clearly less than the denominator, the second factor is less than one,

hence the overall expression is less than 0.5