document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128713>Question 128713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i am having a very hard time grasping this concept<BR>\n" );
document.write( "differentiate two ways: the product rule and then by multiplying the expression before differentiating. can you help me sto solve this problem step by step? thanks in advance\r<BR>\n" );
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document.write( "g(x)=(4x-3)(2x^2+3x+5)<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 #94179 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=94179\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Differentiate by the product rule and then by multiplying then differentiating:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+%284x-3%29%282x%5E2%2B3x%2B5%29 ALIGN=MIDDLE  ALT=\"g%28x%29+=+%284x-3%29%282x%5E2%2B3x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First, let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%284x-3%29 ALIGN=MIDDLE  ALT=\"u+=+%284x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+%282x%5E2%2B3x%2B5%29 ALIGN=MIDDLE  ALT=\"v+=+%282x%5E2%2B3x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The product rule is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx+=+u%2A%28dv%2Fdx%29+%2B+v%2A%28du%2Fdx%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx+=+u%2A%28dv%2Fdx%29+%2B+v%2A%28du%2Fdx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Applying this to your problem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dg%2Fdx+=+%284x-3%29%28d%282x%5E2%2B3x%2B5%29%2Fdx%29%2B%282x%5E2%2B3x%2B5%29%28d%284x-3%29%2Fdx%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Applying the differentiation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dg%2Fdx+=+%284x-3%29%284x%2B3%29%2B%282x%5E2%2B3x%2B5%29%284%29 ALIGN=MIDDLE  ALT=\"dg%2Fdx+=+%284x-3%29%284x%2B3%29%2B%282x%5E2%2B3x%2B5%29%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dg%2Fdx+=+16x%5E2%2B12x-12x-9%2B8x%5E2%2B12x%2B20 ALIGN=MIDDLE  ALT=\"dg%2Fdx+=+16x%5E2%2B12x-12x-9%2B8x%5E2%2B12x%2B20\"   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+=+24x%5E2%2B12x%2B11 ALIGN=MIDDLE  ALT=\"dg%2Fdx+=+24x%5E2%2B12x%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we'll multiply then differentiate:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x-3%29%282x%5E2%2B3x%2B5%29+=+8x%5E3%2B12x%5E2%2B20x-6x%5E2-9x-15 ALIGN=MIDDLE  ALT=\"%284x-3%29%282x%5E2%2B3x%2B5%29+=+8x%5E3%2B12x%5E2%2B20x-6x%5E2-9x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplifying, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+8x%5E3%2B6x%5E2%2B11x-15 ALIGN=MIDDLE  ALT=\"g%28x%29+=+8x%5E3%2B6x%5E2%2B11x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now we'll differentiate:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dg%2Fdx+=+24x%5E2%2B12x%2B11 ALIGN=MIDDLE  ALT=\"dg%2Fdx+=+24x%5E2%2B12x%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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