C3: Differentiation

I had to differentiate

x^3(2x+6)^4

I got down to

8x^3(2x+6)^3 + 3x^2(2x+6)^4

According to the solution bank this is correct but you have to simplify it down afterwards to

2x^2(2x+6)^3(7x+9)

Anyone can explain how that works please?

Your expression contains two terms and both

(2x+6)^3

and

x^2

are factors of both of them. That means we can take

(2x+6)^3

and

x^2

outside the expression:

\displaystyle x^2(2x+6)^3 \left[8x+3(2x+6)\right]

Does this make sense and can you finish the simplification?

OP

Original post by notnek

Your expression contains two terms and both

(2x+6)^3

and

x^2

are factors of both of them. That means we can take

(2x+6)^3

and

x^2

outside the expression:

\displaystyle x^2(2x+6)^3 \left[8x+3(2x+6)\right]

Does this make sense and can you finish the simplification?

Why does the 8x go into the bracket with the higher power?

Original post by Sarabande

Why does the 8x go into the bracket with the higher power?

I don't really understand your question. Could you try to explain again?

Try expanding the expression that I posted and you should see that it is equal to the two terms in your derivative.

OP

I gave it a little thought. It makes perfect sense now. Thanks.

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