Thread: Composite & Quotient Rule -confirm correct answer?

Hi,

I would be really grateful if someone would help me!

With regard to the function f(x) = ln(e^x + e^-x)

By applying the composite rule does this turn into:

1 / e^x+ e^-x ?

And by applying the quotient rule, does the first equation turn into:

e^x + e^ -x / e^x - e^ -x

Many thanks!!!

You don't need to use the quoient rule in this case, consider



In your case and

therefore

Originally Posted by looking0glass

Hi,

I would be really grateful if someone would help me!

With regard to the function f(x) = ln(e^x + e^-x)

By applying the composite rule does this turn into:

1 / e^x+ e^-x ?

And by applying the quotient rule, does the first equation turn into:

e^x + e^ -x / e^x - e^ -x

Many thanks!!!

Please don't just say "turn into"- I would interpret that as meaning a different form of the same equation or function!

The composite rule (also called "chain rule") tells us that the derivative of f(x)= [tex]ln(e^x+ e^{-x})[/itex] is times the derivative of which is .

So the derivative of is , the reciprocal of what you gave.

That derivative is also, by the way, .