SOLUTION: If y=Ax^n, show that x(dy/dx)=ny Thanks!!

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Question 827600: If y=Ax^n, show that x(dy/dx)=ny
Thanks!!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the derivative:
dy%2Fdx+=+n%2AAx%5E%28n-1%29
The desired equation has a y in it. So we want to transform this so that it has a "Ax^n" in it. We almost have that now. But the exponent is n-1, not n. To change the exponent to what we want we will multiply both sides by x:
x%2A%28dy%2Fdx%29+=+x%2A%28n%2AAx%5E%28n-1%29%29
Multiplying the x on the right side times the x^(n-1) we get:
x%2A%28dy%2Fdx%29+=+n%2AAx%5En
and we have the "y" we were looking for:
x%2A%28dy%2Fdx%29+=+n%2Ay
And we're finished.