Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Tough Differentiation Q

Hi, I was wondering how to differentiate cube root 4x^4. Ive tried using the chain rule, but I just cant seem to get the answer?

(edited 7 years ago)

Kevin De Bruyne

Original post by RNVS_99

Hi, I was wondering how to differentiate cube root 4x^4. Ive tried using the chain rule, but I just cant seem to get the answer?

How did you apply the chain rule? Please show working.

Study Forum Helper

Original post by RNVS_99

Hi, I was wondering how to differentiate cube root 4x^4. Ive tried using the chain rule, but I just cant seem to get the answer?

\sqrt[3]{4x^4} = 4^{1/3}\cdot x^{4/3}

Why are you even using the chain rule...?

Original post by RNVS_99

Hi, I was wondering how to differentiate cube root 4x^4. Ive tried using the chain rule, but I just cant seem to get the answer?

Hint:

\sqrt[3]{4x^4} = (4x^4)^\frac{1}{3}

.

Do you see where to go from there?

OP

Original post by RDKGames

\sqrt[3]{4x^4} = 4^{1/3}\cdot x^{4/3}

Why are you even using the chain rule...?

Its a function within a function, so I thought the chain rule would be appropriate, but Im not to sure anyway?

Study Forum Helper

Original post by RNVS_99

Its a function within a function, so I thought the chain rule would be appropriate, but Im not to sure anyway?

You can use the chain rule, sure, but since there is no constant inside this cube root then you can do this instead as it's faster since you can split the terms.

OP

Original post by marioman

Hint:

\sqrt[3]{4x^4} = (4x^4)^\frac{1}{3}

.

Do you see where to go from there?

Thats exactly what I did, but I cant get the answer of 4/3 cube root 4x

username2130115

dy/dx = nx^n-1

OP

Original post by RDKGames

You can use the chain rule, sure, but since there is no constant inside this cube root then you can do this instead as it's faster since you can split the terms.

I still cant manage to get the answer of 4/3 cube root 4x

Study Forum Helper

Original post by RNVS_99

I still cant manage to get the answer of 4/3 cube root 4x

That's not the full answer. Show us your working out.

OP

Original post by RDKGames

That's not the full answer. Show us your working out.

The answer is 4/3 cube root 4x as it says in the book

OP

Original post by RDKGames

That's not the full answer. Show us your working out.

I dont know how to get the answer, which is why I am asking

Study Forum Helper

Original post by RNVS_99

I dont know how to get the answer, which is why I am asking

If you're going with the form I've demonstrated then know that:

\frac{d}{dx}(ax^n)=a \cdot n \cdot x^{n-1}

Show us you applying this to the question.

OP

Original post by RDKGames

If you're going with the form I've demonstrated then know that:

\frac{d}{dx}(ax^n)=a \cdot n \cdot x^{n-1}

Show us you applying this to the question.

So far, my answer is 4/3^-2/3 * 4x/3^1/3
Am I right so far??

Study Forum Helper

Original post by RNVS_99

So far, my answer is 4/3^-2/3 * 4x/3^1/3
Am I right so far??

No. I'm not quite sure why you reduced the exponent on the 4...

\frac{d}{dx}(4^{1/3} \cdot x^{4/3})=4^{1/3} \cdot \frac{4}{3} \cdot x^{1/3}

OP

Original post by RDKGames

No. I'm not quite sure why you reduced the exponent on the 4...

\frac{d}{dx}(4^{1/3} \cdot x^{4/3})=4^{1/3} \cdot \frac{4}{3} \cdot x^{1/3}

ahh okay, I see, cant you then multiply the 4 and the x, giving you the cube root 4x?

Study Forum Helper

Original post by RNVS_99

ahh okay, I see, cant you then multiply the 4 and the x, giving you the cube root 4x?

Indeed. I've misread your previous answer, could help to use latex.

OP

Original post by RDKGames

Indeed. I've misread your previous answer, could help to use latex.

haha, sorry about that, thanks for the help, this question confused me a bit, but now I understand it!

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you

Don't make these mistakes when you're choosing a university

Don't make these mistakes when you're choosing a university

Writing a law personal statement: expert advice from universities

Writing a law personal statement: expert advice from universities

How to get a pupillage (and what to do if you don’t get one)

How to get a pupillage (and what to do if you don’t get one)

Students who got grade 9s at GCSEs share study tips that everyone can follow

Students who got grade 9s at GCSEs share study tips that everyone can follow