# Thread: Finding the slope of the tangent

1. ## Finding the slope of the tangent

$y = x cosx$

How do I find when is the slope of the tangent equal to zero?

2. Originally Posted by looseenz2
$y = x cosx$

How do I find when is the slope of the tangent equal to zero?
Solve $y' = 0$

Differentiate using the product rule

3. Equivalently, the derivative is equal to 0.

So, we calculate the derivative:

$\frac{d}{dx} x \cos x = -x \sin x + \cos x$

Then we set it equal to 0:

$\cos x - x \sin x = 0$

$\cos x = x \sin x$

$\frac{\cos x}{\sin x} = x$

$\cot x = x$

4. So the answer would turn out to be $tan x = \frac{1}{x}$?

5. Originally Posted by looseenz2
So the answer would turn out to be $tan x = \frac{1}{x}$?
That's correct.

6. Ahhh yay! Thank you