document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=460227>Question 460227</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x)=cos nx, find f^(4)[pi/n] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316275 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=316275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the fourth derivative by finding all the other derivatives using the chain rule (there is a pattern).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^'(x) = -n \sin(nx)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{''}(x) = -n^2 \cos(nx)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{'''}(x) = n^3 \sin (nx)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{(4)} (x) = n^4 \cos (nx)\">\r<BR>\n" );
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document.write( "At x = pi/n,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{(4)} (\frac{\pi}{n}) = n^4 \cos (\pi) = -n^4\"> </SPAN>\n" );
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