Differentiate the given function

[1irishman]

Homework Statement

differentiate the following funtion: g(x) = x^3*e^-1/x + 3^x*ln(1/x)

Homework Equations

chain rule and product rule

The Attempt at a Solution

x^3*d/dg(e^-1/x)d/dg(x)^3 + 3^x

sorry...i am very confused!

 

[╔(σ_σ)╝]

In order to serve you better can you please state the chain rule.

 

[1irishman]

In order to serve you better can you please state the chain rule.

yes i think it is:

F'x = f'(g(x))g'(x)

 

[╔(σ_σ)╝]

Lets look at the function g(x) in parts. Let's consider the first part...
x^3(e^(-1/x))

You need the chain rule and the product rule to differentiate this term. Can you try differentiating it again ?

 

[1irishman]

Lets look at the function g(x) in parts. Let's consider the first part...
x^3(e^(-1/x))

You need the chain rule and the product rule to differentiate this term. Can you try differentiating it again ?

Hi, is it the following with a common factor for the first part i mean?

e^-1/x(x^3 + 3x^2)?

 

[╔(σ_σ)╝]

I have no idea of what you just said...

 

[1irishman]

I have no idea of what you just said...

that was my attempt at differntiating the first part.

 

[╔(σ_σ)╝]

How?

Okay what is the derievative of x^3 and of e^(1/x) ?

 

[1irishman]

How?

Okay what is the derievative of x^3 and of e^(1/x) ?

3x^2 and e^-1/x
is that right?

 

[╔(σ_σ)╝]

No. Use the chain rule on e^(-1/x). From your comment it is becoming exceedingly obvious that you do not understand derievatives. Have you considered reviewing your class notes ?

 

[1irishman]

thanks

 

[╔(σ_σ)╝]

I suggest to read up on derievatives and then attempt the problem again. If you still need help post again.

 

[1irishman]

No, i will wait for a more helpful response.

 

[╔(σ_σ)╝]

:-).

 

[1irishman]

Perhaps you should leave your BIG ego at the door before you come into these forums to help people? There's a lot of things many people know that you do not know 'exceedingly well.'

 

[╔(σ_σ)╝]

I am sorry if you feel that way!:-)

I just thought it would be better if you read up on derievatives before attempting the problem.

The derievative of e^(-1/x) is e^(-1/x)*(1/x^2) this is a straight forward application of the chain rule which I asked you for at the outset of this discussion; which you in turn gave me.

Your answer to the question simply revealed that you did not have a firm grasp on derievatives and I was only proposing a remedy to that. :-)

I could give you the answer to the problem in a single post but I felt it was my duty to help you understand things a little better.

 

[theJorge551]

No, what implies the "BIG" ego is your refusal to study up on something you need in order to solve the problem you wish to solve, with the hope of waiting for someone to solve it for you. Use the chain rule on e^-1/x and then apply the product rule.

 

[Dick]

There's nothing wrong with ╔(σ_σ)╝'s advice. Maybe a little abrupt with not going into the chain rule a little more but you are missing it. You've already stated the chain rule f'(g(x))g'(x). In the case of e^(-1/x) that makes f(x)=e^x and g(x)=(-1/x), right? What's the derivative of f and the derivative of g and can you put them into that chain rule formula?

 

[1irishman]

I am sorry as well. I see now what you are saying, and your response has been helpful. :-)

 

[╔(σ_σ)╝]

Follow the last two suggestions given by thejorge551 and dick.

 

[1irishman]

There's nothing wrong with ╔(σ_σ)╝'s advice. Maybe a little abrupt with not going into the chain rule a little more but you are missing it. You've already stated the chain rule f'(g(x))g'(x). In the case of e^(-1/x) that makes f(x)=e^x and g(x)=(-1/x), right? What's the derivative of f and the derivative of g and can you put them into that chain rule formula?

Isn't f(x)=e^-1/x?

 

[1irishman]

Isn't f(x)=e^-1/x?

actually nevermind

 

[1irishman]

-e^x/x^3 ?

 

[╔(σ_σ)╝]

-e^x/x^3 ?

No. Please carefully read dick's post again. Besides, I already gave the answer 2 post ago.

 

[Redbelly98]

Moderator's note: Let's all calm down. I have deleted some posts that contained unnecessary arguing.

1irishman, the derivative of e^(-1/x) would involve taking the derivative of (-1/x), according to the chain rule.