# Gradient of the curve at a point

• Feb 13th 2010, 07:40 AM
jimgreenmore
Gradient of the curve at a point
Find the gradient of the curve $\displaystyle y = x^2 + \frac{1}{x}$ at the point (1,2)

$\displaystyle \frac{dy}{dx} = 2x+x^{-1}$
$\displaystyle =2(1) + (1)^{-1}$
$\displaystyle =2+1$
$\displaystyle = 3$

I've been told this is incorrect, where did I go wrong?
• Feb 13th 2010, 07:44 AM
felper
Quote:

Originally Posted by jimgreenmore
Find the gradient of the curve $\displaystyle y = x^2 + \frac{1}{x}$ at the point (1,2)

$\displaystyle \frac{dy}{dx} = 2x+x^{-1}$
$\displaystyle =2(1) + (1)^{-1}$
$\displaystyle =2+1$
$\displaystyle = 3$

I've been told this is incorrect, where did I go wrong?

You derived wrongly the second factor: $\displaystyle (\frac{1}{x})'=-\frac{1}{x^2}$
• Feb 13th 2010, 07:52 AM
jimgreenmore
Quote:

Originally Posted by felper
You derived wrongly the second factor: $\displaystyle (\frac{1}{x})'=-\frac{1}{x^2}$

Okay, so after re-doing it:

$\displaystyle \frac{dy}{dx} = 2x+-\frac{1}{x^2}$

$\displaystyle =2(1)+-\frac{1}{(1)^2}$

$\displaystyle =2+-\frac{1}{1}$

$\displaystyle =2+-1$

$\displaystyle =1$

Is this the answer?