document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328484>Question 328484</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The total solar radiation H on a particular surface during an average clear day is given by: <BR>\n" );
document.write( "H=5000/T^2+10 \r<BR>\n" );
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document.write( "where t (-6 < equal to or less than t < equal to or less than 6 ) is the number of hours from noon. Note that 6 a.m. is equivalent to t = -6. Find the instantaneous rate of change of H with respect to t at 3 p.m.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235353 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=235353\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ H(t)\ =\ \frac{5000}{t^2\ +\ 10}\">\r<BR>\n" );
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document.write( "Use the Quotient Rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ H'(t)\ =\ \frac{\left(t^2\ +\ 10\right)\ -\ 10000t}{\left(t^2\ +\ 10\right)^2}\">\r<BR>\n" );
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document.write( "You want\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ H'(3)\ =\ \frac{\left((3)^2\ +\ 10\right)\ -\ 10000(3)}{\left((3)^2\ +\ 10\right)^2}\">\r<BR>\n" );
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document.write( "You can do your own arithmetic.\r<BR>\n" );
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document.write( "You can also use the chain rule on this one:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{5000}{t^2\ +\ 10}\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large u\ =\ t^2\ +\ 10\">\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{5000}{u}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{du}\ =\ -\frac{5000}{u^2}\ =\ -\frac{5000}{\left(t^2\ +\ 10\right)^2\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{du}{dt}\ =\ 2t\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \left(\frac{dy}{du}\right)\left(\frac{du}{dt}\right)\ =\ -\frac{10,000t}{\left(t^2\ +\ 10\right)^2\">\r<BR>\n" );
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document.write( "And again, you are seeking the value of\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ H'(3)=\ -\frac{10,000(3)}{\left((3)^2\ +\ 10\right)^2\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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