1. Finding the gradient function.... lost

Hi all,

Firstly I am asked to differentiate y= x^4 - 3x^2 + 6

I get 4x^3 - 6x I am sure this correct, please advise if not

I am lost with the gradient function of this one

y = 3/x^2 - 2x + 5

not sure what to do with the initial fraction

thinking it should be

????? - 2 ??

Cheers

2. Originally Posted by Joel
the gradient function of this one
y = 3/x^2 - 2x + 5
If $y=\frac{c}{f(x)}$ then $y'=\frac{-cf'(x)}{(f(x))^2}$

3. If then

Therefore

y = 3/x^2 - 2x + 5

dy/dx -3 (2x) / (x^2)^2 -2

-6x/x^4 -2 ????

Is this correct?

4. Originally Posted by Joel
Hi all,

Firstly I am asked to differentiate y= x^4 - 3x^2 + 6

I get 4x^3 - 6x I am sure this correct, please advise if not

I am lost with the gradient function of this one

y = 3/x^2 - 2x + 5

not sure what to do with the initial fraction

thinking it should be

????? - 2 ??

Cheers
You need to be less ambiguous. Is it $y = \frac{3}{x^2} - 2x + 5$ or $y = \frac{3}{x^2 - 2x + 5}$?

5. Originally Posted by Joel
Then $y= 3x^{-2}- 2x+ 5$. That's easier than using the quotient rule.

6. .

this would make

y'' = -6xˉ³ - 2 ??