Differentiation problem square root function

[CrossFit415]

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

 

[Mark44]

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

 

[CrossFit415]

Alright

 

[CrossFit415]

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 ?

 

[Mark44]

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]

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, $[-\sqrt{2}, \sqrt{2}]$.

 

[CrossFit415]

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

 

[HallsofIvy]

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

 

[CrossFit415]

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

Sorry!

 

[Mark44]

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).

 

[CrossFit415]

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]

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.