document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945600>Question 945600</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the derivative of the following function using the limt defintion <BR>\n" );
document.write( "((x-1)^2)/(x)<BR>\n" );
document.write( "I can know the answer is 2.(x-1)/(x) but I keep getting it wrong when using the defintion. could you show me step-by-step how to get that final answer?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #576787 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=576787\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the derivative of the following function using the limt defintion <BR>\n" );
document.write( "((x-1)^2)/(x)<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "= (x^2 - 2x + 1)/x<BR>\n" );
document.write( "= x - 2 + (1/x)<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "You can probably do the x term --> 1<BR>\n" );
document.write( "The -2 --> 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "That leaves 1/x<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(1/(x+h) - 1/x)/h = (x - (x+h))/(h*(x^2 + hx))<BR>\n" );
document.write( "= -h/(h*(x^2 + hx))<BR>\n" );
document.write( "= -1/(x^2 + hx)<BR>\n" );
document.write( "Lim = -1/x^2<BR>\n" );
document.write( "=====================<BR>\n" );
document.write( "--> 1 - (1/x^2)<BR>\n" );
document.write( "or (x^2 - 1)/x^2 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );