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# Help on C3 Differentiation Pls watch

1. The question is: Find the set of values of x for which f'(x)<0
2. (Original post by AxSirlotl)
The question is: Find the set of values of x for which f'(x)<0
The first step is obviously to get an expression for f'(x), have you managed to do that?
3. (Original post by Plagioclase)
The first step is obviously to get an expression for f'(x), have you managed to do that?
yeah boii
4. (Original post by AxSirlotl)
The question is: Find the set of values of x for which f'(x)<0
You have to use the quotient rule and then look at the numerator.

5. (Original post by AxSirlotl)
yeah boii
Well then, you've got your inequality, you just need to solve that.
You have to use the quotient rule and then look at the numerator.

I got
Sorry, I can't do proper fractions because I don't understand the guide heh
7. (Original post by AxSirlotl)
I got
Sorry, I can't do proper fractions because I don't understand the guide heh
Your derivative is wrong. To write a fraction it's \frac{numerator}{denominator}, but the notation you're using is acceptable anyway.
8. (Original post by NotNotBatman)
Your derivative is wrong. To write a fraction it's \frac{numerator}{denominator}, but the notation you're using is acceptable anyway.
Does TSR detect LaTex automatically? We tried replying with the coding:

\frac{x}{x^2+2}

&

[tex]\frac{x}{x^2+2}
Does TSR detect LaTex automatically? We tried replying with the coding:

\frac{x}{x^2+2}

&

[tex]\frac{x}{x^2+2}
[tex] maths things go here [/ tex] , but without the space after the /
10. (Original post by NotNotBatman)
Your derivative is wrong. To write a fraction it's \frac{numerator}{denominator}, but the notation you're using is acceptable anyway.
I keep getting the same answer ;-;

I tried doing fractions but it kept putting my numerator in front of my fraction and leaving the top of the fraction blank, so I can't really show my working very easily.
11. (Original post by AxSirlotl)
I keep getting the same answer ;-;

I tried doing fractions but it kept putting my numerator in front of my fraction and leaving the top of the fraction blank, so I can't really show my working very easily.
Thanks for the LaTex tip!

Problem: differentiate

Technique: quotient rule

u = x and v = X^2+2, u' = derivative of u and v'= derivative of v
12. Use the chain rule for differentiation:

h(x) = f(x)/g(x)

h'(x) = f'(x)g(x)-f(x)g'(x) / [g(x)]^2

The last step is trivial; let the inequality be less than 0 and solve it accordingly.
13. Is that or
14. (Original post by zeldor711)
Is that or
The latter
Thanks for the LaTex tip!

Problem: differentiate

Technique: quotient rule

u = x and v = X^2+2, u' = derivative of u and v'= derivative of v
(Original post by thekidwhogames)
Use the chain rule for differentiation:

h(x) = f(x)/g(x)

h'(x) = f'(x)g(x)-f(x)g'(x) / [g(x)]^2

The last step is trivial; let the inequality be less than 0 and solve it accordingly.
I got my derivative as -1/(x^2+2), is that right ;-;
16. (Original post by AxSirlotl)
I got my derivative as -1/(x^2+2), is that right ;-;
Not quite.

If you post your working we would just be able to spot where you're going wrong.
17. (Original post by RDKGames)
Not quite.

If you post your working we would just be able to spot where you're going wrong.
Using the quotient rule:

u = x v = x^2 + 2

u' = 1 v' = 2x

Then I got
numerator: (x^2 + 2) - 2x^2

denominator: (x^2 + 2)^2

So on the top I had v x u' - u x v' all over v^2
18. (Original post by AxSirlotl)
Using the quotient rule:

u = x v = x^2 + 2

u' = 1 v' = 2x

Then I got
numerator: (x^2 + 2) - 2x^2

denominator: (x^2 + 2)^2

So on the top I had v x u' - u x v' all over v^2
OK, so how did you go from to ?
19. (Original post by RDKGames)
OK, so how did you go from to ?
I've just realised that's wrong, I mean I've had another go at it and I'm back to (-x^2 + 2)/(x^2+2)^2
I'm not sure where to go from there, if I need make that into an inequality then I'm not sure what to do after that.
20. (Original post by AxSirlotl)
I've just realised that's wrong, I mean I've had another go at it and I'm back to (-x^2 + 2)/(x^2+2)^2
I'm not sure where to go from there, if I need make that into an inequality then I'm not sure what to do after that.
so

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