# Thread: finding the slope of a tangent line

1. ## finding the slope of a tangent line

I have been stuck on this question for a while now. I need to find the slope of the tangent to the curve 5 over the square root of x (5/squarerootX)

2. ## Re: finding the slope of a tangent line

start by rewriting $\displaystyle y = \frac{5}{\sqrt{x}}$ so that you may use the power rule for derivatives

$\displaystyle y = 5x^{-1/2}$

continue ...

3. ## Re: finding the slope of a tangent line

When I use the power rule I get (-5/2) (x^-3/2) if i did that right i am still going to have a radical so how will I find the slope?
I'm sorry for coming off as such an amateur, but calc is the bane of my existence

4. ## Re: finding the slope of a tangent line

Originally Posted by neontiger94
When I use the power rule I get (-5/2) (x^-3/2) if i did that right i am still going to have a radical so how will I find the slope?
I'm sorry for coming off as such an amateur, but calc is the bane of my existence
You don't. The tangent at $\displaystyle \left(x_0,\frac{5}{\sqrt{x_0}}\right)$ is $\displaystyle y-\frac{5}{\sqrt{x_0}}=\frac{-5}{2\sqrt{x_0^3}}(x-x_0)$

5. ## Re: finding the slope of a tangent line

Thats what I thought the answer was, but maybe I didnt specify the question properly. The question reads Find the slope m of the tangent to the curve
y = 5/square root x

at the point where x = a > 0.
does this help at all, beacuse I think I'm supposed to find the exact slope using the derivative as a function

6. ## Re: finding the slope of a tangent line

Originally Posted by neontiger94
Thats what I thought the answer was, but maybe I didnt specify the question properly. The question reads Find the slope m of the tangent to the curve
y = 5/square root x at the point where x = a > 0.
does this help at all, beacuse I think I'm supposed to find the exact slope using the derivative as a function
Always post the complete problem.

But that changes nothing in what I posted. Just let $\displaystyle a=x_0$ and you are done.

7. ## Re: finding the slope of a tangent line

Okay thank you I should have used the power rule from the beginning