document.write( "Question 1200825: If y(x) = ln(secx + tanx), determine the third derivative of y(x), i.e., find d^3y/dx^3. \n" ); document.write( "
Algebra.Com's Answer #835119 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"y%28x%29+=+ln%28sec%5E%22%22%28x%29%5E%22%22%5E%22%22+%2B+tan%5E%22%22%28x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Use the formulas: \"d%2F%28dx%29\"\"ln%28u%29\"\"%22%22=%22%22\"\"%28du%2Fdx%29%2Fu%5E%22%22\", \r\n" );
document.write( "  \"d%2F%28dx%29\"\"sec%5E%22%22%28u%29\"\"%22%22=%22%22\"\"sec%5E%22%22%28u%29tan%5E%22%22%28u%29expr%28du%2Fdx%29\",\r\n" );
document.write( "and \"d%2F%28dx%29\"\"tan%5E%22%22%28u%29\"\"%22%22=%22%22\"\"sec%5E2%28u%29expr%28du%2Fdx%29\"\r\n" );
document.write( "\r\n" );
document.write( "we have:\r\n" );
document.write( "\r\n" );
document.write( "\"dy%2Fdx\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"dy%2Fdx\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"dy%2Fdx\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"dy%2Fdx=sec%5E%22%22%28x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d%5E2y%2Fdx%5E2=sec%5E%22%22%28x%29tan%5E%22%22%28x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"d%5E3y%2Fdx%5E3=sec%5E3%28x%29%2Btan%5E2%28x%29sec%5E%22%22%28x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d%5E3y%2Fdx%5E2=sec%5E%22%22%28x%29%28sec%5E2%28x%29%2Btan%5E2%28x%29%5E%22%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "Use formula \"1%2Btan%5E2%28u%29=sec%5E2%28u%29\" as \"tan%5E2%28u%29=sec%5E2%28u%29-1\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"d%5E3y%2Fdx%5E2=sec%5E%22%22%28x%29%28sec%5E2%28x%29%2Bsec%5E2%28x%29%5E%22%22-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d%5E3y%2Fdx%5E2=sec%5E%22%22%28x%29%282sec%5E2%28x%29%5E%22%22-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );