Differentiation problem! square root function

  • #1
160
0
I'm on mobile so I can't use latex.

Differentiate:

g(x)=√(4-x^4) , x is a set of [-√2, √2] and determine the domains.

So I got the derivative which is,

g'(x)=(-4x^3) ^1/2

What should I do with the -+√2 ?

I don't know what to do next
 

Answers and Replies

  • #2
33,722
5,418
I'm on mobile so I can't use latex.

Differentiate:

g(x)=√(4-x^4) , x is a set of [-√2, √2] and determine the domains.

So I got the derivative which is,

g'(x)=(-4x^3) ^1/2
Nope. You need to use the chain rule. It will help to write your function as
g(x) = (4 - x4)^(1/2)
What should I do with the -+√2 ?

I don't know what to do next
 
  • #4
160
0
I have

g'(x) = 1/2(4-x)^-1/2 • -4x^3

Then how would I determine the domains? I know 4-x^4 >= 0. So what about the two square roots?

What should I do with the +/-√2 ?
 
Last edited:
  • #5
33,722
5,418
It's still not right. Check your work.

Since your original is named g, its derivative is g', not G'.

The domain of g is the interval [-[itex]\sqrt{2}[/itex], [itex]\sqrt{2}[/itex]]. The domain of the this derivative will be exactly the same, with the possible exception of the endpoints.
 
  • #6
HallsofIvy
Science Advisor
Homework Helper
41,833
956
I have

G'(x) = 1/2(4-x)^-1/2 • -4x^3
NO. Do it again and show each step.

Then how would I determine the domains? I know 4-x^4 >= 0. So what about the two square roots?

What should I do with the +/-√2 ?
The domain will be the intersection of the natural domain of the derivative (not what you have above) and the given domain of the function, [itex][-\sqrt{2}, \sqrt{2}][/itex].
 
  • #7
160
0
g'(x) = 1/2(4-x^4)^1/2-1 • d/dx (4-x^4)
= 1/2(4-x^4)^-1/2 • -4x^3
Should I keep continuing?

Then
= -2x^3(4-x^4)^-1/2
 
Last edited:
  • #8
HallsofIvy
Science Advisor
Homework Helper
41,833
956
Please do NOT use "x" both as the variable and for multiplication!
 
  • #10
33,722
5,418
g'(x) = 1/2(4-x^4)^1/2-1 • d/dx (4-x^4)
= 1/2(4-x^4)^-1/2 • -4x^3
Should I keep continuing?

Then
= -2x^3(4-x^4)^-1/2
Much better.

When you write expressions on a single line, you need to use more parentheses. The above should be written as -2x^3(4-x^4)^(-1/2).
 
  • #11
160
0
Much better.

When you write expressions on a single line, you need to use more parentheses. The above should be written as -2x^3(4-x^4)^(-1/2).
Thanks! Ohh ok I ll be sure to use more parenthesis next time.

So should I just plug in +/- √2 for x to find the domains? Or leave it alone? Are the domains just +/- √2 ?
 
  • #12
33,722
5,418
So should I just plug in +/- √2 for x to find the domains? Or leave it alone? Are the domains just +/- √2 ?
Your question was answered twice in this thread.

I don't think you understand what "domain" means - it's not domains. The domain (singular) is the set of numbers at which the relevant function is defined.
 

Related Threads on Differentiation problem! square root function

  • Last Post
Replies
2
Views
2K
Replies
4
Views
4K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
3
Views
578
  • Last Post
Replies
9
Views
2K
Replies
6
Views
540
  • Last Post
Replies
2
Views
5K
Replies
5
Views
26K
  • Last Post
Replies
2
Views
1K
Top