differentiate with 'e's

[Guest]

How do you do this:

differentiate: f(x)= x^e + e^x
ans is: ex^(e-1) + e^x

How do you know when to use the ln thing? like put ln on both sides to make it easier?

 

[stapel]

The number "e" is, in the end, just a number. Apply the usual rule: "d(xⁿ)/dx = nx^n-1".

You should have been given a rule for y = e^x.

You generally only use logarithmic differentiation when the variable is in both the base and the power, such as "y = x^3x".

Eliz.

 

[Guest]

oh so the deriative for y = e^x is just the same thing. So that wors for all es to the power of a varible? or just any number to the power of a varible?

 

[stapel]

oh so the deriative for y = e^x is just the same thing.

"Just the same thing" as what? I mentioned two different rules. Please clarify your question.

So that wors for all es to the power of a varible? or just any number to the power of a varible?

I'm sorry, but I don't know what this means...?

Eliz.

 

[Guest]

the derivative of y = e^x is e^x? e^(to an expodent)'s derivative is e^(to an expodent)'s?

 

[stapel]

the derivative of y = e^x is e^x?

Yes.

e^(to an expodent)'s derivative is e^(to an expodent)'s?

Not necessarily. If the exponent is anything other than just "x", then the Chain Rule will apply.

Eliz.

 

[Guest]

oh okay thanks