document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032383>Question 1032383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the derivatives of the following functions: <BR>\n" );
document.write( "(a) f(x) =&#8730;x cos x\r<BR>\n" );
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document.write( "(b) g(x) = (x^3 + 1) /  (sin x)\r<BR>\n" );
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document.write( "(c) h(x) = e^x sin(2x) \r<BR>\n" );
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document.write( "(d) k(x) = (x^2) / (log x)<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 #647052 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=647052\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the derivatives of the following functions: <BR>\n" );
document.write( "(a) f(x) = sqrt(x)*cos(x)<BR>\n" );
document.write( "f'(x) = d/dx(sqrt(x))*cos(x) = sqrt(x)*d/dx(cos(x))<BR>\n" );
document.write( "= (1/2)/sqrt(x)*cos(x) - sqrt(x)*sin(x)<BR>\n" );
document.write( "= 2sqrt(x)*cos(x)/x - sqrt(x)*sin(x)<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "(b) g(x) = (x^3 + 1) /  (sin x)<BR>\n" );
document.write( "g(x) = (x^3+1)*csc(x)<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "(c) h(x) = e^x sin(2x)<BR>\n" );
document.write( "Too easy.<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "(d) k(x) = (x^2) / (log x) --- assuming natural logs<BR>\n" );
document.write( "k(x) = x^2*(log(x))^-1<BR>\n" );
document.write( "k'(x) = 2x*(log(x))^-1 + x^2*(-1)*(log(x))^-2*(1/x)<BR>\n" );
document.write( "= 2x/ln(x) - x/(ln(x))^2\r<BR>\n" );
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