How to Differentiate a Cubic Root Function with a Square Expression Inside?

[Mary4ever]

Homework Statement

Differentiate:

Homework Equations

y=∛((7-3x^2)^2)

The Attempt at a Solution

y^'(x)=(4x(3x^2-7))/(∛((7-3x^2 )^2))^2 )

 

[Mark44]

Homework Statement

Differentiate:

Homework Equations

y=∛((7-3x^2)^2)

The Attempt at a Solution

y^'(x)=(4x(3x^2-7))/(∛((7-3x^2 )^2))^2 )

It's much more convenient to write your function as y = (7 - 3x²)^2/3. When you're differentiating, it's almost always better to rewrite expressions with radicals using exponents. Your answer might be correct, but if so, it needs to be simplified.

 

[Mary4ever]

I really need to know if it is correct, could you please let me know if it is?

 

[tiny-tim]

(try using the X² button just above the Reply box )

y^'(x)=(4x(3x^2-7))/(∛((7-3x^2 )^2))^2 )

that looks correct, but it needs simplifying

(also, it's a ridiculous way of writing it, and you'll lose marks in the exam if you do that)

 

[Mary4ever]

Thank you for you reply. So what would be the correct way to write it so I do not lose marks for it?

 

[tiny-tim]

first, simplify it, as Mark44 suggested

 

[Mary4ever]

Is this correct: y = (((7-3x^2)^2))^ (1/3)
dy/dx = (1/3) (((7-3x^2)^2))^ (-2/3) (2(7-3x^2)(-6x))
= (24/9)(7x - 3x^3) / ∛((7-3x^2)^4)

 

[tiny-tim]

Is this correct: y = (((7-3x²)²))^(1/3)

i'm sorry, but can't you see how ridiculous that is?

why not just write y = (7-3x²)^2/3 ?

 

[Mary4ever]

ok so is this a correct final answer now: y'(x)=4x(3x^2-7) ??

 

[cmcraes]

The solution is

12x(3x^(2)-7) isn't it?

 

[cmcraes]

Sorry never mind thought you said derivative not differentiate!

 

[tiny-tim]

ok so is this a correct final answer now: y'(x)=4x(3x^2-7) ??

how did you get that?

 

[Mark44]

The solution is

12x(3x^(2)-7) isn't it?

No.

Sorry never mind thought you said derivative not differentiate!

You get the derivative when you differentiate a function. It seems that you didn't know this.

 

[Mary4ever]

I am really confused now, what is the correct answer then?

 

[Mark44]

I am really confused now, what is the correct answer then?

This was the advice I gave in post #2.

It's much more convenient to write your function as y = (7 - 3x²)^2/3. When you're differentiating, it's almost always better to rewrite expressions with radicals using exponents. Your answer might be correct, but if so, it needs to be simplified.

What do you get if you differentiate the function that I wrote? You need to use the chain rule (correctly).

 

[Mary4ever]

Differentiating the function you wrote would get: y'(x)=12x^3-28x
Is this correct? Please help

 

[tiny-tim]

no

show us, step-by-step, how you got that