document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=987646>Question 987646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given functions f and g satisfying <BR>\n" );
document.write( "f(3) = 3,    g(3) = 2,    f &#8242;(3) = 4    and    g &#8242;(3) = 2<BR>\n" );
document.write( "find the values of the following derivatives.\r<BR>\n" );
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document.write( "(f . g)&#8242;(3) =<BR>\n" );
document.write( "(f / g)&#8242;(3) =\r<BR>\n" );
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document.write( "THANK YOU :-)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #608372 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=608372\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (f * g)(x) = f(x)*g(x)\r<BR>\n" );
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document.write( "(f * g)'(x) = [f(x)*g(x)]' ... apply the derivative\r<BR>\n" );
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document.write( "(f * g)'(x) = f ' (x)*g(x) + f(x)*g ' (x) ... use the product rule\r<BR>\n" );
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document.write( "(f * g)'(3) = f ' (3)*g(3) + f(3)*g ' (3) ... plug in x = 3\r<BR>\n" );
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document.write( "(f * g)'(3) = 4*2 + 3*2 ... make the proper substitutions (based on the values given)\r<BR>\n" );
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document.write( "(f * g)'(3) = 8+6\r<BR>\n" );
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document.write( "(f * g)'(3) = 14\r<BR>\n" );
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document.write( "(f/g)(x) = f(x)/g(x)\r<BR>\n" );
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document.write( "(f/g)'(x) = [f(x)/g(x)]'  ... apply the derivative\r<BR>\n" );
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document.write( "(f/g)'(x) = [f ' (x)*g(x) - f(x)*g ' (x)]/[g(x)]^2  ... use the quotient rule\r<BR>\n" );
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document.write( "(f/g)'(3) = [f ' (3)*g(3) - f(3)*g ' (3)]/[g(3)]  ... plug in x = 3\r<BR>\n" );
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document.write( "(f/g)'(3) = [4*2 - 3*2]/[2^2] ... make the proper substitutions (based on the values given)\r<BR>\n" );
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document.write( "(f/g)'(3) = (8-6)/4\r<BR>\n" );
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document.write( "(f/g)'(3) = 2/4\r<BR>\n" );
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document.write( "(f/g)'(3) = 1/2 </SPAN>\n" );
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