document.write( "Question 353582: find the derivative of the function\r
\n" ); document.write( "\n" ); document.write( "\"y+=+2+%5E+%28sin%28pi%2Ax%29%29\"
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Algebra.Com's Answer #252639 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\"y+=+2+%5E+%28sin%28pi%2Ax%29%29\"
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\n" ); document.write( "Take natural logs of both sides\r
\n" ); document.write( "\n" ); document.write( "\"ln%28y%29+=+ln%282+%5E+%28sin%28pi%2Ax%29%29%29\"\r
\n" ); document.write( "\n" ); document.write( "Use a rule of logarithms of exponentials on the right side:\r
\n" ); document.write( "\n" ); document.write( "\"ln%28y%29+=+sin%28pi%2Ax%29ln%282%29\"\r
\n" ); document.write( "\n" ); document.write( "\"ln%28y%29+=+ln%282%29sin%28pi%2Ax%29\"\r
\n" ); document.write( "\n" ); document.write( "[I wrote it that way so your would recognize that ln(2) is just a constant.]\r
\n" ); document.write( "\n" ); document.write( "Find the derivative of both sides, remembering that ln(2) is just a
\n" ); document.write( "constant and that we must use the chain rule on the right side by
\n" ); document.write( "taking the derivitive of the \"inside\":\r
\n" ); document.write( "\n" ); document.write( "\"%28dy%2Fdx%29%2Fy+=+ln%282%29cos%28pi%2Ax%29%2Api\"\r
\n" ); document.write( "\n" ); document.write( "\"%28dy%2Fdx%29%2Fy+=+pi%2Aln%282%29cos%28pi%2Ax%29\"\r
\n" ); document.write( "\n" ); document.write( "Multiply both sides by y\r
\n" ); document.write( "\n" ); document.write( "\"dy%2Fdx+=+y%2Api%2Aln%282%29cos%28pi%2Ax%29\"\r
\n" ); document.write( "\n" ); document.write( "To get the derivative in terms of x only, we go back to
\n" ); document.write( "the original equation \"y+=+2+%5E+%28sin%28pi%2Ax%29%29\" and
\n" ); document.write( "substitute for y\r
\n" ); document.write( "\n" ); document.write( "\"dy%2Fdx+=+%282+%5E+%28sin%28pi%2Ax%29%29%29%2Api%2Aln%282%29cos%28pi%2Ax%29\"\r
\n" ); document.write( "\n" ); document.write( "Writing the constants first, and the more complicated factor last:\r
\n" ); document.write( "\n" ); document.write( "\"dy%2Fdx+=+pi%2Aln%282%29cos%28pi%2Ax%292+%5E+%28sin%28pi%2Ax%29%29\" \n" ); document.write( "
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