# Gradient of the curve at a point

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

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

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

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

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

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

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

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

Okay, so after re-doing it:

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

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

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

$=2+-1$

$=1$