A quotient rule question; and a proof one at that! f(x) = x/(1 + x^2)^{1/2}

A

Astronomer_X

New member
Joined
Mar 2, 2019
Messages
9
https://ibb.co/2sJdHQC This is my question.

https://ibb.co/2sJdHQC And here is my attempt.

So I can recognise that this is a quotient rule function that then requires application of the chain rule in order to differentiate and get into the form requested. I have either made a mistake in my execution of the quotient rule, or I have done something stupid in how I am collecting like terms. Either way, if anyone here can help me out on how to go about this, I would be very grateful
 
Try that definition of "v", again. It seems it is only partly there.
 
I cannot read your picture. What is the function to be differentiated?
 
The derivative of a constant is not the constant (unless the constant is 0)
You defined v wrong and then based on your definition of v you did not find the correct dv/dx
 
You showed your work twice, rather than first showing the problem itself. You appear to be differentiating [MATH]\frac{x}{\sqrt{2+x^2}}[/MATH].

But in your work, you sometimes have [MATH]2 + x^2[/MATH], and sometimes [MATH]2x + x^2[/MATH]. Which is it?
 
Dr.Peterson said:
You showed your work twice, rather than first showing the problem itself. You appear to be differentiating [MATH]\frac{x}{\sqrt{2+x^2}}[/MATH].

But in your work, you sometimes have [MATH]2 + x^2[/MATH], and sometimes [MATH]2x + x^2[/MATH]. Which is it?
Click to expand...
Apologies, that was a stupid mistake.
 
Astronomer_X said:
https://ibb.co/2sJdHQC This is my question.

https://ibb.co/2sJdHQC And here is my attempt.

So I can recognise that this is a quotient rule function that then requires application of the chain rule in order to differentiate and get into the form requested. I have either made a mistake in my execution of the quotient rule, or I have done something stupid in how I am collecting like terms. Either way, if anyone here can help me out on how to go about this, I would be very grateful
Click to expand...
BTW, you recognized that this require the quotient rule, but you used the product rule
 
You must log in or register to reply here.
Top