document.write( "Question 827600: If y=Ax^n, show that x(dy/dx)=ny \r
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Algebra.Com's Answer #498977 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
Start with the derivative:
\n" ); document.write( " $\"dy%2Fdx+=+n%2AAx%5E%28n-1%29\"$
\n" ); document.write( "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:
\n" ); document.write( " $\"x%2A%28dy%2Fdx%29+=+x%2A%28n%2AAx%5E%28n-1%29%29\"$
\n" ); document.write( "Multiplying the x on the right side times the x^(n-1) we get:
\n" ); document.write( " $\"x%2A%28dy%2Fdx%29+=+n%2AAx%5En\"$
\n" ); document.write( "and we have the \"y\" we were looking for:
\n" ); document.write( " $\"x%2A%28dy%2Fdx%29+=+n%2Ay\"$
\n" ); document.write( "And we're finished. \n" ); document.write( "

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