document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203615>Question 1203615</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me with this Calculus problem? I am finding this problem hard to solve. After a few steps, I am stuck and don't know how to proceed to find the derivative.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839319 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839319\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A basic application of the product rule for derivatives tells us<br><BR>\n" );
document.write( "(d/dx)((f(x)e^x)) = f(x)e^x+f'(x)e^x<br><BR>\n" );
document.write( "So in this problem probably the easiest way to find h'(x) is to write f(x)=(3x-12)(x^4-x^(1/2)) and find the derivative using that pattern.<br><BR>\n" );
document.write( "f(x) = (3x-12)(5x^4-x^(1/2)) = 15x^5-60x^4-3x^(3/2)+12x^(1/2)<br><BR>\n" );
document.write( "f'(x) = 75x^4-240x^3-(9/2)x^(1/2)+6x^(-1/2)<br><BR>\n" );
document.write( "f(x)+f'(x) = 15x^5+15x^4-240x^3-3x^(3/2)+(15/2)x^(1/2)+6x^(-1/2)<br><BR>\n" );
document.write( "And so<br><BR>\n" );
document.write( "ANSWER: h'(x) = (15x^5+15x^4-240x^3-3x^(3/2)+(15/2)x^(1/2)+6x^(-1/2))<br><BR>\n" );
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