You are Here: Home >< Maths

# general maths question help watch

1. how do you show that:

cos(sin^-1 x) = ±√(1-x^2), where ^-1 -> inverse
2. let u = sin-1 x
x = sinu
cos u = rt(1 - sin²u)
3. or draw a right-angled triangle with opposite length x and hypotenuse 1
4. (Original post by Fermat)
let u = sin-1 x
x = sinu
cos u = rt(1 - sin²u)
how dumb of me! i was so depressed about that that i couldn't sleep! aghhh...i tried integrating and all this werid crap, lol

cheers

pk
5. need help with another maths quesiton form problem sheet 2:

show that:

dn(xn)=n!
dxn

any ideas?

cheers

PK
6. (Original post by Phil23)
need help with another maths quesiton form problem sheet 2:

show that:

dn(xn)=n!
dxn

any ideas?

cheers

PK
Let y = xn:

dy/dx = nxn-1
d2y/dx2 = n(n-1)xn-2
d3y/dx3 = n(n-1)(n-2)x(n-3)
...

The nth derivative will leave x0, because each time the power will be reduced by one. So the result will be [n(n-1)(n-2)...(3)(2)(1)] x x0 = n!

It's not really a proof as such, but it shows how the result falls out.
7. (Original post by Phil23)
need help with another maths quesiton form problem sheet 2:

show that:

dn(xn)=n!
dxn

any ideas?

cheers

PK
You could use induction to find the kth derivative of and then set , showing that the term is
You could guess and prove that the kth derivative of is
Obviously then setting gives
8. (Original post by Gaz031)
You could use induction to find the kth derivative of and then set , showing that the term is
You could guess and prove that the kth derivative of is
Obviously then setting gives
#the prob is that the function varies with the derivative...according to the sheet..i.e. 10th derivative of x^10, and 9th of x^9 etc...so a bit lost...tried doing a generalised chain rule, but not got anywhere yet

pk

must be easier than induction
9. (Original post by Phil23)
#the prob is that the function varies with the derivative...according to the sheet..i.e. 10th derivative of x^10, and 9th of x^9 etc...so a bit lost...tried doing a generalised chain rule, but not got anywhere yet

pk

must be easier than induction
How does that matter? If you let then you obviously have the nth derivative of which can mean the 10th derivative of , the 9th derivative of ... and so on for any positive integer n.
Of course, you could just 'explain why' but perhaps this way is more likely to be regarded as a proper proof.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: July 8, 2005
Today on TSR

### University open days

• University of Roehampton
Sat, 17 Nov '18
• Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 17 Nov '18
• Bournemouth University
Sat, 17 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams