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carel
Posts:
161
Registered:
12/12/04


Derivative a*x^n
Posted:
Feb 4, 2008 6:23 AM


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^(n1)
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^(n1)
Carel



