document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078501>Question 1078501</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Please help me solve this equation:\r<BR>\n" );
document.write( "\n" );
document.write( "1. Determine dy/dx for y = x&#8730;x(5x^2 &#8722; 3)^4<BR>\n" );
document.write( "(There is no need to simplify the answer.)<BR>\n" );
document.write( "2. For the curve defined by the equation x^2 &#8722; xy + y^2 = 3<BR>\n" );
document.write( "(a) Show that <BR>\n" );
document.write( "dy/dx =2x &#8722; y/x &#8722; 2y<BR>\n" );
document.write( "(b) Find the equation of the normal to the curve at the point (&#8722;1, 1). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692947 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=692947\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=f%2Ag ALIGN=MIDDLE  ALT=\"y=f%2Ag\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=x ALIGN=MIDDLE  ALT=\"f=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g=sqrt%28x%285x%5E2-3%29%5E4%29 ALIGN=MIDDLE  ALT=\"g=sqrt%28x%285x%5E2-3%29%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=f%2A%28dg%2Fdx%29%2Bg%2A%28df%2Fdx%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=f%2A%28dg%2Fdx%29%2Bg%2A%28df%2Fdx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdx=1 ALIGN=MIDDLE  ALT=\"df%2Fdx=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dg%2Fdx=%281%2F2%29%28x%285x%5E2-3%29%5E4%29%5E%28-1%2F2%29%2A%28x%2A4%285x%5E2-3%29%5E3%2A10x%2B%285x%5E2-3%29%5E4%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=dg%2Fdx=%281%2F2%29%28x%285x%5E2-3%29%5E4%29%5E%28-1%2F2%29%2A%28x%2A4%285x%5E2-3%29%5E3%2A10x%2B%285x%5E2-3%29%5E4%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=dg%2Fdx=%281%2F2%29%28%285x%5E2-3%29%5E3%2F%28sqrt%28x%285x%5E2-3%29%5E4%29%29%29%2810x%5E2%2B5x%5E2-3%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=dg%2Fdx=%281%2F2%29%28%285x%5E2-3%29%5E3%2F%28sqrt%28x%285x%5E2-3%29%5E4%29%29%29%2810x%5E2%2B5x%5E2-3%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=dg%2Fdx=%281%2F2%29%28%285x%5E2-3%29%5E3%2F%28sqrt%28x%285x%5E2-3%29%5E4%29%29%29%2815x%5E2-3%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=dg%2Fdx=%283%2F2%29%28%285x%5E2-3%29%5E3%2F%28sqrt%28x%285x%5E2-3%29%5E4%29%29%29%285x%5E2-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%28%283x%29%2F2%29%28%285x%5E2-3%29%5E3%2F%28sqrt%28x%285x%5E2-3%29%5E4%29%29%29%285x%5E2-1%29%2Bsqrt%28x%285x%5E2-3%29%5E4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2a. Differentiate implicitly,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xdx-%28xdy%2Bydx%29%2B2ydy=0 ALIGN=MIDDLE  ALT=\"2xdx-%28xdy%2Bydx%29%2B2ydy=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%2B2y%29dy%2B%282x-y%29dx=0 ALIGN=MIDDLE  ALT=\"%28-x%2B2y%29dy%2B%282x-y%29dx=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2y%29dy=%282x-y%29dx ALIGN=MIDDLE  ALT=\"%28x-2y%29dy=%282x-y%29dx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%282x-y%29%2F%28x-2y%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=%282x-y%29%2F%28x-2y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2b. The slope of the tangent line is equal to the value of the derivative at the point. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bt%5D=+%282%28-1%29-1%29%2F%28-1-2%281%29%29+=+%28-3%29%2F%28-3%29=1 ALIGN=MIDDLE  ALT=\"m%5Bt%5D=+%282%28-1%29-1%29%2F%28-1-2%281%29%29+=+%28-3%29%2F%28-3%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The tangent and normal line are perpendicular to each other so their slopes are negative reciprocals.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bn%5D%2Am%5Bt%5D=-1 ALIGN=MIDDLE  ALT=\"m%5Bn%5D%2Am%5Bt%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bn%5D=-1 ALIGN=MIDDLE  ALT=\"m%5Bn%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then using the point-slope form of  a line,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1=-1%28x-%28-1%29%29 ALIGN=MIDDLE  ALT=\"y-1=-1%28x-%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1=-%28x%2B1%29 ALIGN=MIDDLE  ALT=\"y-1=-%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1=-x-1 ALIGN=MIDDLE  ALT=\"y-1=-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bn%5D=-x ALIGN=MIDDLE  ALT=\"y%5Bn%5D=-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=gg2.JPG\">.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );