document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=59407>Question 59407</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please find derivative and simplify:\r<BR>\n" );
document.write( "\n" );
document.write( "y=  x^3ln3x\r<BR>\n" );
document.write( "\n" );
document.write( "y=  e^ln5x\r<BR>\n" );
document.write( "\n" );
document.write( "y=  e^lnx\r<BR>\n" );
document.write( "\n" );
document.write( "y=  ln(5x+2)^3/ln(5x+2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i've completed over half of my homework, but i'm stuck right here...please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #40704 by </B><A HREF=/tutors/aboutme.mpl?userid=uma><B>uma(370)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=uma><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=40704\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">     (i) y = x^3 ln3x<BR>\n" );
document.write( "This is a product and we apply product rule.<BR>\n" );
document.write( "dy/dx = x^3 (1/3x)(3) + ln3x * 3x^2 [Derivative of lnx = 1/x]<BR>\n" );
document.write( "      = x^2 + 3x^2 ln3x [on simplifying]<BR>\n" );
document.write( "      = x^2(1 + 3ln3x)\r<BR>\n" );
document.write( "\n" );
document.write( "(ii) y = e^ln5x<BR>\n" );
document.write( "       = 5x  [because e^lnx = x only]<BR>\n" );
document.write( "dy/dx = 5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(iii) y = e^lnx<BR>\n" );
document.write( "        = x<BR>\n" );
document.write( "dy/dx = 1\r<BR>\n" );
document.write( "\n" );
document.write( "(iv) I believe the question is y = [ln(5x+2)^3]/ln(5x+2)\r<BR>\n" );
document.write( "\n" );
document.write( "                                 = 3ln(5x+2)/ln(5x+2) [property of ln]<BR>\n" );
document.write( "                                 = 3<BR>\n" );
document.write( "So dy/dx = 0\r<BR>\n" );
document.write( "\n" );
document.write( "Good Luck!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );