Differentiate. (Assume k is a constant.)

y = 1 / (p + ke^p)

I tried using the quotient rule...
(f/g)' = (gf' - fg') / g^2

and ended up with
(1-pke^(p-1)) / (p+ke^p)^2

which is apparently wrong.

Question

Differentiate. (Assume k is a constant.)

y = 1 / (p + ke^p)

I tried using the quotient rule...
(f/g)' = (gf' - fg') / g^2

and ended up with 
(1-pke^(p-1)) / (p+ke^p)^2

which is apparently wrong.

ash2326 · Answer

Are we differentiating with respect to p?

anonymous · Answer

@ash2326  That was all the information I was given :|

ash2326 · Answer

ok, if k is constant then we are differentiating with respect to p.
We have e^p in the denominator, that's one place you made a mistake.
Do you know differentiation of e^x?

anonymous · Answer

@ash2326 e^x --> e^x

Hmm... standby, going to take another shot at this

ash2326 · Answer

yes, I'm here

anonymous · Answer

So deriving (p+ke^p) I end up with (1+pke^p)

Everything then looks like
 
(0 - (1+pke^p)) / (p+ke^p)^2

Is there any further I can take this?

anonymous · Answer

Aside from (-1-pke^p) in the numerator

ash2326 · Answer

differentiation of p+ke^p has a small mistake, it should be this
$$\frac{d}{dp}(p+ke^P)=1+ke^p$$

anonymous · Answer

Huh. Looks like I confused myself and mixed the power rule in there.

Thanks for all of your help!

ash2326 · Answer

Do you understand?