# Please verify my working for quotient and chain rule differentiation

#### BinaryBoy

Hi everyone,

I've been trying to solve a quite complex equation using both the chain rule and the quotient rule of differentiation. I think I have a handle on the first part of the equation (the top row), but please see the attached document with my full working and verify that I am correct. Secondly, I am unsure how to proceed with solving the equation after that, since I have to manipulate the (bottom squared) part and I am unsure whether I need to expand using chain rule, or simply expand. So any help solving this problem will be much appreciated! Here is the attached full workings: As you can see, I now need to work with the (bottom squared) portion of the equation. I am unsure how to proceed.

Many thanks,

Nathaniel

#### Prove It

MHF Helper
First of all, if $$\displaystyle \displaystyle u = 5(2x^2 + 3)^3$$ then $$\displaystyle \displaystyle u' = 60x(2x^2 + 3)^2$$

and if $$\displaystyle \displaystyle v = 3(4x^3 - 1)^2$$ then $$\displaystyle \displaystyle v' = 72x^2(4x^3 - 1)$$.

• BinaryBoy

#### BinaryBoy

Thanks Prove It. I'll make the modifications and perform the calculations again. But once I've done that, will I need to differentiate the (bottom squared) part before expanding?

#### BinaryBoy

UPDATE:

I think I've incorporated Prove It's corrections, and am again up to the last section of the equation where I need to take the squared bottom part of the equation into account.

Here are my current workings and where I am up to: From there, how do I finish solving the equation? Do I need to differentiate the bottom, or expand it normally? Or is the answer correct as it is?

Many thanks,

Nathaniel