document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125287>Question 1125287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I have a problem with the algebra of getting the derivative of: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=x%28sqrt%2816-x%5E2%29%29 ALIGN=MIDDLE  ALT=\"h%28x%29=x%28sqrt%2816-x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So far I know it uses product and chain rule \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28d%2Fdx%29%28x%29+%2816-x%5E2%29%5E%281%2F2%29+%2B+%28x%29+%28d%2Fdx%29%2816-x%5E2%29%5E%281%2F2%29+%28d%2Fdx%29%2816-x%5E2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%29%2816-x%5E2%29%5E%281%2F2%29+%2B%28x%29%28%281%2F2%29%2816-x%5E2%29%5E%28-1%2F2%29%29+%28-2x%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From here my work is definetly wrong if I didn't miss any rules: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2816-x%5E2%29%5E%281%2F2%29%2B%28-2x%5E2%29%28%281%2F2%29%2816-x%5E2%29%5E%28-1%2F2%29%29+ ALIGN=MIDDLE  ALT=\"+%2816-x%5E2%29%5E%281%2F2%29%2B%28-2x%5E2%29%28%281%2F2%29%2816-x%5E2%29%5E%28-1%2F2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Put everything over 2 due to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%2816-x%5E2%29%5E%281%2F2%29%2B%28-2x%5E2%29%2816-x%5E2%29%5E%28-1%2F2%29%29%2F%282%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then I took out/factored out : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816-x%5E2%29%5E%28-1%2F2%29%7D%7D%0D%0A%0D%0A%7B%7B%7B+%28%2816-x%5E2%29%5E%28-1%2F2%29+%281-2x%5E2%29%2F%282%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "moving the negative down, then I get for a final answer of \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-2x%5E2%29%2F+2%28%2816-x%5E2%29%5E%281%2F2%29%29+ ALIGN=MIDDLE  ALT=\"%281-2x%5E2%29%2F+2%28%2816-x%5E2%29%5E%281%2F2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  which is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281-2x%5E2%29%2F+2sqrt%2816-x%5E2%29 ALIGN=MIDDLE  ALT=\"+%281-2x%5E2%29%2F+2sqrt%2816-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But the answer is actually: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2x%5E2-16%29%2F2sqrt%2816-x%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28-2x%5E2-16%29%2F2sqrt%2816-x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28x%5E2-8%29%2F2sqrt%2816-x%5E2%29 ALIGN=MIDDLE  ALT=\"-2%28x%5E2-8%29%2F2sqrt%2816-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I'm certain by algebra is messed up somewhere, most likely when I factored but I can't find what I did wrong. I'm very confused since my teacher can easily do it in a few steps but I got lost very fast. Any help would be really great if possible!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741598 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=741598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Large number of steps to show.\r<BR>\n" );
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document.write( "Using the Product Rule, and working through, one of the steps becomes, for derivative,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816-x%5E2%29-x%5E2%2Fsqrt%2816-x%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2816-x%5E2%29-x%5E2%2Fsqrt%2816-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplifying further gives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816-2x%5E2%29%2Fsqrt%2816-x%5E2%29 ALIGN=MIDDLE  ALT=\"%2816-2x%5E2%29%2Fsqrt%2816-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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