document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160095>Question 1160095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a) Let f(x)= sqrt(9+6x^2) Find f ' (x)<BR>\n" );
document.write( "(b) Let f(x)= e^sqrt(9+6x^2) Find f ' (x)   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #783252 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=783252\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "(a) \r<BR>\n" );
document.write( "\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+sqrt%289%2B6x%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+sqrt%289%2B6x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" > ' <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "apply the chain rule:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28df%2Au%29%2F%28dx%29=%28df%2Fdu%29%28du%2Fdx%29 ALIGN=MIDDLE  ALT=\"%28df%2Au%29%2F%28dx%29=%28df%2Fdu%29%28du%2Fdx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=sqrt%28u%29 ALIGN=MIDDLE  ALT=\"f=sqrt%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=9%2B6x%5E2 ALIGN=MIDDLE  ALT=\"u=9%2B6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29=%28d%2Fdu%29%28u%29+%2A%28d%2Fdx%29%289%2B6x%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%29=%28d%2Fdu%29%28u%29+%2A%28d%2Fdx%29%289%2B6x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdu%29%28u%29=1%2F%282sqrt%28u%29%29 ALIGN=MIDDLE  ALT=\"%28d%2Fdu%29%28u%29=1%2F%282sqrt%28u%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%289%2B6x%5E2%29=12x ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%289%2B6x%5E2%29=12x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29=%281%2F%282sqrt%28u%29%29%29%2A12x ALIGN=MIDDLE  ALT=\"%28x%29=%281%2F%282sqrt%28u%29%29%29%2A12x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substitute back <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=9%2B6x%5E2 ALIGN=MIDDLE  ALT=\"u=9%2B6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+ ALIGN=MIDDLE  ALT=\"f+\"   DISABLED_style= \"max-width:90%; height:auto;\" >' <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29=%281%2F%282sqrt%289%2B6x%5E2%29%29%29%2A12x ALIGN=MIDDLE  ALT=\"%28x%29=%281%2F%282sqrt%289%2B6x%5E2%29%29%29%2A12x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29=12x%2F%282sqrt%289%2B6x%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28x%29=12x%2F%282sqrt%289%2B6x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29=6x%2F%28sqrt%289%2B6x%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28x%29=6x%2F%28sqrt%289%2B6x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(b) \r<BR>\n" );
document.write( "\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+e%5Esqrt%289%2B6x%5E2%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=+e%5Esqrt%289%2B6x%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "apply the chain rule:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28df%2Au%29%2F%28dx%29=%28df%2Fdu%29%28du%2Fdx%29 ALIGN=MIDDLE  ALT=\"%28df%2Au%29%2F%28dx%29=%28df%2Fdu%29%28du%2Fdx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=e%5Eu ALIGN=MIDDLE  ALT=\"f=e%5Eu\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=sqrt%289%2B6x%5E2%29 ALIGN=MIDDLE  ALT=\"u=sqrt%289%2B6x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29=%28d%2Fdu%29%28e%5Eu%29+%2A%28d%2Fdx%29%28sqrt%289%2B6x%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28x%29=%28d%2Fdu%29%28e%5Eu%29+%2A%28d%2Fdx%29%28sqrt%289%2B6x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdu%29%28e%5Eu%29+=e%5Eu ALIGN=MIDDLE  ALT=\"%28d%2Fdu%29%28e%5Eu%29+=e%5Eu\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%28sqrt%289%2B6x%5E2%29%29=6x%2Fsqrt%289%2B6x%5E2%29 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%28sqrt%289%2B6x%5E2%29%29=6x%2Fsqrt%289%2B6x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >' <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29=e%5Eu%2A%286x%2Fsqrt%289%2B6x%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28x%29=e%5Eu%2A%286x%2Fsqrt%289%2B6x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........substitute back <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=sqrt%289%2B6x%5E2%29 ALIGN=MIDDLE  ALT=\"u=sqrt%289%2B6x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C%22%22%2C%28x%29=e%5Esqrt%289%2B6x%5E2%29%2A%286x%2Fsqrt%289%2B6x%5E2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C%22%22%2C%28x%29=%286x%2Ae%5Esqrt%289%2B6x%5E2%29%29%2Fsqrt%289%2B6x%5E2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );