Thread: bracket expansion and differentiation

need to multiply

(x^2-1)^4

I get

-20x^9+32x^7-12x^5

Then i need to differentiate this 4 times

d^4/dx^4 (-20x^9+32x^7-12x^5)

I get

-10080x^6+6720x^4-720x^2

Is this right?

Originally Posted by ubhik

need to multiply

(x^2-1)^4

I get

-20x^9+32x^7-12x^5

Then i need to differentiate this 4 times

d^4/dx^4 (-20x^9+32x^7-12x^5)

I get

-10080x^6+6720x^4-720x^2

Is this right?

Think about this. Your highest power in the expansion will be . So you can't be right.

By the binomial theorem:


You have and :

Thus


(I'd recommend making sure you know how to do it the long way as well. It's good practice.)

And make sure you take 4 derivatives. You only took 3.

-Dan

ok so for the differentiation of
[(x^2 - 1)^4]

i got


1680x^4 - 1440x^2 + 144


Is this right now?

Hello, ubhik!

I got: .

Is this right now? . . . . Yes!

Good for you!

Originally Posted by ubhik

ok so for the differentiation of
[(x^2 - 1)^4]

i got


1680x^4 - 1440x^2 + 144


Is this right now?

[(x^2 - 1)^4] is an octic, so its derivative is a septic, so whatever anyone else says its derivative cannot be a quartic.

RonL

Originally Posted by ubhik

ok so for the differentiation of
[(x^2 - 1)^4]

i got


1680x^4 - 1440x^2 + 144


Is this right now?

RonL

Thank you, thats great, but I need to differentiate it 4 times, not just once and then, the other answer is correct...

Originally Posted by ubhik

Thank you, thats great, but I need to differentiate it 4 times, not just once and then, the other answer is correct...

did the instructions tell you to expand the brackets first? i'd use the chain rule (as CaptainBlack did) 4 times and forget about binomial expansion.