# Differentiation problem! square root function

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

Related Calculus and Beyond Homework Help News on Phys.org
Mark44
Mentor
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

Alright

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:
Mark44
Mentor
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 [-$\sqrt{2}$, $\sqrt{2}$]. The domain of the this derivative will be exactly the same, with the possible exception of the endpoints.

HallsofIvy
Homework Helper
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, $[-\sqrt{2}, \sqrt{2}]$.

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:
HallsofIvy
Homework Helper
Please do NOT use "x" both as the variable and for multiplication!

Please do NOT use "x" both as the variable and for multiplication!
Sorry!

Mark44
Mentor
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).

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 ?

Mark44
Mentor
So should I just plug in +/- √2 for x to find the domains? Or leave it alone? Are the domains just +/- √2 ?