document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328647>Question 328647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please find the derivatives of the function given by\r<BR>\n" );
document.write( "\n" );
document.write( "y=4e^((x^3)+1)\r<BR>\n" );
document.write( "\n" );
document.write( "please show working </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235460 by </B><A HREF=/tutors/aboutme.mpl?userid=galactus><B>galactus(183)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=galactus><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=galactus><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=235460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the derivative of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ae%5E%28x%5E3%2B1%29 ALIGN=MIDDLE  ALT=\"4%2Ae%5E%28x%5E3%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "This requires the chain rule. To put it simply, the chain rule is the derivative of the inside times the derivative of the outside.\r<BR>\n" );
document.write( "\n" );
document.write( "What is the outside?. It is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ae%5E%28x%5E3%2B1%29 ALIGN=MIDDLE  ALT=\"4%2Ae%5E%28x%5E3%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "What is the inside?. It is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B1 ALIGN=MIDDLE  ALT=\"x%5E3%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Derivative of outside is just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ae%5E%28x%5E3%2B1%29 ALIGN=MIDDLE  ALT=\"4%2Ae%5E%28x%5E3%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Derivative of inside: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now, multiply them: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2A4e%5E%28x%5E3%2B1%29=12x%5E2e%5E%28x%5E3%2B1%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2A4e%5E%28x%5E3%2B1%29=12x%5E2e%5E%28x%5E3%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "That's it. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );