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# C2 Indices help watch

1. Given that y = 2x root(x) + 2 root(x) / x

Show that dy/dx = x-1 / x root(x)

Any help?
Thanks
2. simplify the terms by combining the powers ? remember that the square root power is 1/2 ?
3. (Original post by orange8120)
Given that y = 2x root(x) + 2 root(x)
----------------------------
x

Show that dy/dx = x-1
------------
x root(x)

Any help?
Thanks
Simplify y to: then differentiate.
4. (Original post by Zacken)
Simplify y to: then differentiate.
So after I differentiate I get x^-1/2 - x ^-3/2.
How do I simplify that to x-1 / x root(x)

Many thanks
5. (Original post by orange8120)
So after I differentiate I get x^-1/2 - x ^-3/2.
How do I simplify that to x-1 / x root(x)

Many thanks
So you have:

Remember that:
6. (Original post by Zacken)
So you have:

Remember that:
Thanks a lot. Also i'm strugglng with:

root(x) - 1 / x^2

Find gradient when x = 2.
I get that i need to differentiate and then sub in 2 as x but no matter how many times I do it I can't get the right answer.
7. (Original post by orange8120)
Thanks a lot. Also i'm strugglng with:

root(x) - 1 / x^2

Find gradient when x = 2.
I get that i need to differentiate and then sub in 2 as x but no matter how many times I do it I can't get the right answer.
Again, first thing first - simplify, then differentiate:

What do you get when you differentiate that?
8. (Original post by Zacken)
Again, first thing first - simplify, then differentiate:

What do you get when you differentiate that?
-3/2x +2x^-3
9. (Original post by orange8120)
-3/2x +2x^-3
See bolded bit. You need to subtract one from the power. What is ?

What's ?
10. (Original post by Zacken)
See bolded bit. You need to subtract one from the power. What is ?

What's ?
-3/2x^-5/2 + 2x^-3
11. (Original post by orange8120)
-3/2x^-5/2 + 2x^-3
And what do you get when you put into that?
12. (Original post by Zacken)
And what do you get when you put into that?
-3/2(2^-5/2) + 2(2^-3) = -0.0152
13. (Original post by orange8120)
-3/2(2^-5/2) + 2(2^-3) = -0.0152
That's correct, in't it?
14. (Original post by Zacken)
That's correct, in't it?
Yes it is! Thank you so so much!
15. (Original post by orange8120)
Yes it is! Thank you so so much!
No problemo!

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