Hello,

I am wondering how to differentiate an equation when I have a power of x and a constant in the denominator, for example:

y=a/(e^(x+b)+c), where a,b,c are any number bar zero.

I could do it easily without that c there, but this has me stumpped.

Just use the quotient rule.

\frac{a}{e^{x+b}+c}

Quotient rule:

\frac{(e^{x+b}+c)(0)-(a)(e^{x+b})}{(e^{x+b}+c)^{2}}

Now, simplify.

Do it again for the second derivative.

I thank you for your help once again kind sir.

I am now testing your advice to see whether I can apply it to my problem, however, I have yet another question.

I was under the impression that the quotient rule can only be used when there are powers of x in both the numerator and denominator, was I misinformed?

There are powers of x. x^0.

Ah, but of course. Thank you Capuchin.

There is one thing I'd like to clarify though.

I wouldn't use the quotient rule for something like a/x, however, I must use it in my question which is basically a/(x+b).

Is it due to this b value that I now need to use the quotient rule?

No, the b is just a constant. You use the quotient rule when you have a quotient.

You could also use the product rule.

a(e^{x+b}+c)^{-1}

Product rule:

a(-1)(e^{x+b}+c)^{-2}(e^{x+b})-(e^{x+b}+c)^{-1}(0)

Simplify and you'll get the same result as with the quotient rule.