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saram
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#1
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#1
Is sin^x(x) the same as (sinx)^x?

Or would it be sin^2(x) = sin(sinx) and (sinx)^2 = sinxsinx
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J.F.N
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#2
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(Original post by saram)
Is sin^x(x) the same as (sinx)^x?

Or would it be sin^2(x) = sin(sinx) and (sinx)^2 = sinxsinx
sin^x(x) is (sinx)^x. So for example, sin^2 x = (sinx)^2 = sinx.sinx. Its NOT sin(sinx).
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saram
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#3
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And what about f^2(x) and [f(x)]^2??

Are they the same?
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dvs
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Personally I've never seen f^2(x) used before. Although the notation f^n(x) (nth derivative of f(x)) comes to mind, but the second derivative is expressed as f''(x) and not f^2(x). [f(x)]^2 on the other hand is the square of f(x).
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J.F.N
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(Original post by saram)
And what about f^2(x) and [f(x)]^2??

Are they the same?
f^2(x) is f(f(x)) (function composition), and [f(x)]^2 is just the function squared. So, for example, if f(x)=x-1 then f^2(x)=f(f(x))=f(x-1)=x-2.
On the other hand, [f(x)]^2 = (x-1)^2=x^2 -2x + 1
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J.F.N
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(Original post by dvs)
Personally I've never seen f^2(x) used before. Although the notation f^n(x) (nth derivative of f(x)) comes to mind, but the second derivative is expressed as f''(x) and not f^2(x). [f(x)]^2 on the other hand is the square of f(x).
Its function composition notation, not for derivatives.
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dvs
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#7
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(Original post by J.F.N)
Its function composition notation, not for derivatives.
You learn something new every day.
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saram
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#8
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#8
Yeah, I thought so Thank you very much!!
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