What Is the Correct Derivative of the Function y(r) = (r^2 - 5.50r)exp(-r)?

[justin335]

Homework Statement

Consider the following function of the variable r, r>/=0
y(r)=(r^(2)-5.50r)exp(-r)
Find the value of the first derivative dy/dr at r=5.50

Homework Equations

How do I solve this? I know its a simple derivative equation, but I can't seem to get it. I tried finding the derivative and then plugging in r=5.50 but MasteringPhysics says it incorrect.
Also, does exp(-r) mean to the -r power? I've never seen it written like that.

The Attempt at a Solution

Assuming exp(-r) means to the negative r power...
I tried using the chain rule;
y(r)=(r^(2)-5.50r)exp(-r)
dy/dr=-r(r^(2)-5.50r)^(-r-1)*(2r-5.50)
plugging in r=5.50, I get a 0, making the solution 0, which is obviously wrong...
I think its my poor calc skills, any help would be great, thanks!

 

[TSny]

exp(-r) is a representation of ##e^{-r}##.

So, your function is ##y(r) = (r^2-5.50r)e^{-r}##

 

[justin335]

exp(-r) is a representation of ##e^{-r}##.

So, your function is ##y(r) = (r^2-5.50r)e^{-r}##

Thanks, would the derivative be e^-r(2r^3-16.5r^2+30.35r)? Thats what I got, and after subbing in r=5.5 again, I still get the answer wrong...

 

[Chestermiller]

Thanks, would the derivative be e^-r(2r^3-16.5r^2+30.35r)? Thats what I got, and after subbing in r=5.5 again, I still get the answer wrong...

What's the derivative of e^x with respect to x?

What's the derivative of e^-x with respect to x?

Do you know how to differentiate by parts?

 

[justin335]

What's the derivative of e^x with respect to x?

What's the derivative of e^-x with respect to x?

Do you know how to differentiate by parts?

Oh ok, Ill have to reference my calc notes since I am pretty rusty. but I think I should get it now. Thanks for the help