document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=366556>Question 366556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evening All, <BR>\n" );
document.write( "Right its been a while since i have attempted maths, and have just gone back to further ed. I have attempted the following questions, which im sure should be simple, but of course like anything its just getting back into things after a number of years. i have listed the questions below, and my answers if anybody will take the time to have a quick look and correct me where neccessary i would appreciate this.\r<BR>\n" );
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document.write( "1)Find dy/dx by differentiating with respect to x the following expressions.\r<BR>\n" );
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document.write( "a) y=x^3-6x^2+9x-1 = 3x^2-12x+8<BR>\n" );
document.write( "b) y=1/2x -sqrtx = 1/2-1/2x^-1/2<BR>\n" );
document.write( "c) y=e^x-e^-x = e^x+e^-x<BR>\n" );
document.write( "d) y=25cosx--sinx = -25sinx-cosx<BR>\n" );
document.write( "e) y= 3sinhx-4coshx = 3hsinhx+4hsinhx<BR>\n" );
document.write( "f) y= (x^2+1) sinhx = 1\r<BR>\n" );
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document.write( "2 Use product rule to obtain dy/dx for the following\r<BR>\n" );
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document.write( "a) y=x^2e^x = 2x(e^x)+x^2(e^x)<BR>\n" );
document.write( "b) y= xtanx = 1(tanx)+x(sec^2x)<BR>\n" );
document.write( "c) y= x^4ln(x)= 4x^3(ln(x))+x^4(1/x)<BR>\n" );
document.write( "d) y= x^2sinx = 2x(sinx)+x^2(cosx)<BR>\n" );
document.write( "e) y= e^-xcosx = -e^-x(cos x)+ e^-x (-sinx)<BR>\n" );
document.write( "f) y=(x^2+1)sinhx = (2x +1) (sinhx)+(x^2+1)(cosh x)\r<BR>\n" );
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document.write( "Finally, use the quotient rule to differentiate with respect to x, simplifying as far as possible.<BR>\n" );
document.write( "a) y= sinx/1+e^-x = 1+e^-x(cosx)-(1-e^x)sinx/(1+e^-x)^2\r<BR>\n" );
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document.write( "b) y= lnx/1+x^2 = 1+x^2(1/x)-1+2x(ln x)/(1+x^2)^2\r<BR>\n" );
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document.write( "Really this would be appreciated thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #261230 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=261230\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)Find dy/dx by differentiating with respect to x the following expressions. <BR>\n" );
document.write( "a) y=x^3-6x^2+9x-1 = 3x^2-12x+8  *** + 9<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "b) y=1/2x -sqrtx = 1/2-1/2x^-1/2 = (x - sqrt(x))/2x (same answer)<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "c) y=e^x-e^-x = e^x+e^-x<BR>\n" );
document.write( "d) y=25cosx--sinx = -25sinx-cosx ** there are 2 minus signs??<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "e) y= 3sinhx-4coshx = 3hsinhx+4hsinhx Is it sin(hx), or hyperbolic?<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "f) y= (x^2+1) sinhx = 1 <BR>\n" );
document.write( "2 Use product rule to obtain dy/dx for the following <BR>\n" );
document.write( "a) y=x^2e^x = 2x(e^x)+x^2(e^x)<BR>\n" );
document.write( "b) y= xtanx = 1(tanx)+x(sec^2x)<BR>\n" );
document.write( "c) y= x^4ln(x)= 4x^3(ln(x))+x^4(1/x) = 4x^3*ln(x) + x^3<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "d) y= x^2sinx = 2x(sinx)+x^2(cosx)<BR>\n" );
document.write( "e) y= e^-xcosx = -e^-x(cos x)+ e^-x (-sinx)<BR>\n" );
document.write( "f) y=(x^2+1)sinhx = (2x +1) (sinhx)+(x^2+1)(cosh x)<BR>\n" );
document.write( "Not (2x + 1) *****<BR>\n" );
document.write( "= 2x*sinh(x) + (x^2+1)*cosh(x)<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Finally, use the quotient rule to differentiate with respect to x, simplifying as far as possible.<BR>\n" );
document.write( "a) y= sinx/1+e^-x = 1+e^-x(cosx)-(1-e^x)sinx/(1+e^-x)^2 <BR>\n" );
document.write( "b) y= lnx/1+x^2 = 1+x^2(1/x)-1+2x(ln x)/(1+x^2)^2 <BR>\n" );
document.write( " </SPAN>\n" );
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