document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1093885>Question 1093885</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Choose a composite trigonometric function of the form h(x) = g(f(x)) where the function g is one of the trigonometric functions and f is any function more complicated than y = x.<BR>\n" );
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document.write( "Note: An example of an appropriate function h would be h(x) = sin(3x – 4). However, you must pick a function other than this example for this task.<BR>\n" );
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document.write( "1.  Show the step-by-step computation of the correct derivative of h(x) using the chain rule.\r<BR>\n" );
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document.write( "2.  Using the function h you constructed for part A, find the instantaneous rate of change at x = &#960;/3.<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 #708500 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=708500\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Choose a composite trigonometric function of the form h(x) = g(f(x)) where the function g is one of the trigonometric functions and f is any function more complicated than y = x.\r<BR>\n" );
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document.write( "Note: An example of an appropriate function h would be h(x) = sin(3x – 4). However, you must pick a function other than this example for this task.<BR>\n" );
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document.write( "Let g(x) = cos(x)<BR>\n" );
document.write( "Let f(x) = 6x+20<BR>\n" );
document.write( "Then h(x) = g(f(x)) = g(6x+20) = cos(6x+20)<BR>\n" );
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document.write( "1. Show the step-by-step computation of the correct derivative of h(x) using the chain rule.<BR>\n" );
document.write( "h'(x) = -sin(6x+20)*6 = -6sin(6x+20)<BR>\n" );
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document.write( "2. Using the function h you constructed for part A, find the instantaneous rate of change at x = &#960;/3.<BR>\n" );
document.write( "h'(pi/3) = -6sin(6(pi/3)+20) = -6sin(20) = -6*0.9129 = -5.4777<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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