document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032805>Question 1032805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find  the derivatives of the following functions<BR>\n" );
document.write( "(a) f(x) = sqrt x cos x ( sqrt is only on x ) <BR>\n" );
document.write( "(b) g(x) = (x^3 + 1)/sin x<BR>\n" );
document.write( "(c) h(x) = e^x sin(2x) (d) k(x) = x^2 / log x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647427 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=647427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=ewatrrr&illustration_name=trig_D\">. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=ewatrrr&illustration_name=derivative_ruless\">.<BR>\n" );
document.write( "apply respective rules:<BR>\n" );
document.write( "f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+x%29+cos+%28x%29+ ALIGN=MIDDLE  ALT=\"sqrt%28+x%29+cos+%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > |Apply Multiplication Rule<BR>\n" );
document.write( "f' = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29%2F2sqrt%28x%29+-+sqrt%28x%29sin%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29%2F2sqrt%28x%29+-+sqrt%28x%29sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3+%2B+1%29%2Fsin+%28x%29+ ALIGN=MIDDLE  ALT=\"%28x%5E3+%2B+1%29%2Fsin+%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  |Apply Division Rule<BR>\n" );
document.write( "g' = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283x%5E2sinx+-+%28x%5E3+%2B+1%29cos%28x%29%29%2Fsin%5E2%28x%29%29%29+or+%7B%7B%7B%7B%7B%7B+%283x%5E2%2Fsin%28x%29+-+%28x%5E3+%2B+1%29cos%28x%29%29%2Fsin%5E2%28x%29%29%29%0D%0Ah%28x%29+=+%7B%7B%7Be%5Ex+sin%282x%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >   |Apply Multiplication Rule / chain rule<BR>\n" );
document.write( "h' = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28e%5Ex%29+cos%282x%29+%2B+%28e%5Ex%29+sin%282x%29 ALIGN=MIDDLE  ALT=\"2%28e%5Ex%29+cos%282x%29+%2B+%28e%5Ex%29+sin%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  0r <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28e%5Ex%29%28sin%282x%29+%2B+2cos%282x%29%29 ALIGN=MIDDLE  ALT=\"%28e%5Ex%29%28sin%282x%29+%2B+2cos%282x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "k(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2F+log+x ALIGN=MIDDLE  ALT=\"x%5E2+%2F+log+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  |Apply Division Rule<BR>\n" );
document.write( "k' = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282xln%28x%29+-+x%5E2%281%2Fx%29%29%2Fln%5E2%28x%29+ ALIGN=MIDDLE  ALT=\"+%282xln%28x%29+-+x%5E2%281%2Fx%29%29%2Fln%5E2%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Fln%28x%29+-+x%2Fln%5E2%28x%29 ALIGN=MIDDLE  ALT=\"2x%2Fln%28x%29+-+x%2Fln%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );