Finding equation of line tangent to curve

• January 23rd 2013, 06:47 AM
togo
Finding equation of line tangent to curve
seem to have a problem with basic differentiation:

Question: y = 1/(x^2 + 1)
At point x = 1, y = 1/2

Work:
(x^2+1)^-1
-1(X^2+1)^-2 (2x)
(-x^2-1)^-2 (2x)
(-(1)^2 - 1)^-2(2(1)

however, 1 - 1 = 0 and applying ^2 means you are dividing two by zero? where did I go wrong, thanks.
• January 23rd 2013, 07:28 AM
hollywood
Re: Finding equation of line tangent to curve
Two problems: You changed $-1(x^2+1)^{-2}$ to $(-x^2-1)^{-2}$, which is not correct, and when you plugged in x=1 to $-x^2$, you multiplied by -1 first and then squared, which again is not correct.

The correct answer is:
$-1(x^2+1)^{-2} (2x) = -\frac{2x}{(x^2+1)^2} = -\frac{2}{(1+1)^2} = -\frac{1}{2}$

- Hollywood
• January 23rd 2013, 09:33 AM
togo
Re: Finding equation of line tangent to curve
but (1+1)^2 = 4? oh nm... ofc when I really look at it I see after posting :(