Question

Derivative of the following:

F(x)= ((3x^2 -2)^2)/x^2

Answer 1

okay to make this easier
you want to bring the x² to the top
when you do this, the power changes to negative so you get

(3x²-2)²x^-2

multiply out of the brackets
then differentiate as normal

can you do this?

Answer 2

or you could use the product rule

Answer 3

I'm still confused

Answer 4

are you familiar with chain rule and product rule ?

Answer 5

Yes I am.

Answer 6

Just not exactly when they are together

Answer 7

so applying these

f'(x) = 6x*2(3x^2 - 2) * x^-2 + (3x^2 - 2)^2 * -2x^-3

Answer 8

product rule d(uv)/dx = u*dv/dx + v*(du/dx)

Answer 9

second thoughts - its probably a little easier to use the quotient rule!!

Answer 10

d(u/v)/ dx = [ v du/dx - u dv/dx] v^2 where u and v are functions of x

f'(x) = x^2* 12x(3x^2 - 2) - (3x^2-2)^2 * 2x
----------------------------------
x^4

which needs to be simplified

Answer 11

Hmmmmm not following

Answer 12

is it the differentiation of (3x^2 - 2)^2 that you are not following?

Answer 13

- you use chain rule to do this

Answer 14

do you use the f'(x) notation or dy/dx?

Answer 15

F'(x)

Answer 16

ok chain rule states that

(fg(x)' = f'(g)x * g'(x)

here g(x) = 3x^2 - 2 and fg(x) = 3(x^2 - 2)^2

g'(x) = 6x right?

Answer 17

Yes

Answer 18

and f'(g)x = 2(3x^2 - 2)

so multiplying give 12x(3x^2 - 2)