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Topic: Derivative a*x^n
Replies: 3   Last Post: Feb 4, 2008 11:30 AM

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carel

Posts: 161
Registered: 12/12/04
Derivative a*x^n
Posted: Feb 4, 2008 6:23 AM
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Hi Group

Is my proof new or just a variation of known stuff.

Alternative proof to the dirivative of y = a*x^n which is dy/dx =
a*n*x^(n-1)

Let e = the natural base 2.718281828.....

Now let x = e^u , so that y = a* e^(u*n) , then we have dx/du = e^u ,
so that du/dx = 1/e^u = 1/x

Note also that u = ln(x) , so the above is also a proof that the
derivative of ln(x) is 1/x

So dy/dx = dy/du * du/dx = a*n*[e^(u*n)] * 1/x

So dy/dx = a*n*(x^n) *1/x = a*n*x^(n-1)

Carel



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