So, what is the difference between cos^3 x, cos x^3 and (cos x)^3 or is there even a difference in between them?

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- Dec 5th 2012, 08:43 AMameerulislamdifference between cos^3 x and cos x^3?
So, what is the difference between cos^3 x, cos x^3 and (cos x)^3 or is there even a difference in between them?

Thanks - Dec 5th 2012, 08:56 AMtopsquarkRe: difference between cos^3 x and cos x^3?
- Dec 5th 2012, 11:42 AMskeeterRe: difference between cos^3 x and cos x^3?
note that some calculators have the syntax to mean , and to mean .

- Dec 6th 2012, 07:32 AMameerulislamRe: difference between cos^3 x and cos x^3?
ok what about cos5x^1/2 , can I move 5 like this 5 cos x^1/2 ?

Thanks again. - Dec 6th 2012, 07:46 AMPlatoRe: difference between cos^3 x and cos x^3?
- Dec 6th 2012, 07:50 AMameerulislamRe: difference between cos^3 x and cos x^3?
- Dec 6th 2012, 09:16 AMHallsofIvyRe: difference between cos^3 x and cos x^3?
No! neither , which is what I think you mean, nor , which is what you actually wrote, is equal to . The first

**means**"find the square root of x, then take the cosine of that number, then multiply it by itself 5 times". The second**means**"find the square root of x, multiply that by 5, then take the cosine". The last**means**"find the square root of x, find the cosine of it, then multiply by 5".

For example, if x= 4, so that (approximately) so that , approximately. Of course, . Of course, so .

Those are three different calculations giving three different answers. - Dec 6th 2012, 10:56 AMameerulislamRe: difference between cos^3 x and cos x^3?
- Dec 6th 2012, 11:21 AMHallsofIvyRe: difference between cos^3 x and cos x^3?
The

**chain**rule! which we can write as , with and . and so that which is very similar to what you have except that it is still in terms of v, not u. To get apply the chain rule again: . Since v= 5x, so .

Of course, you could also do that as one "chain rule": . - Dec 6th 2012, 02:41 PMskeeterRe: difference between cos^3 x and cos x^3?