document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=366198>Question 366198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evening All, 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(cpsx)-(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 #261237 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=261237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1a)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=3x%5E2-12x%2Bhighlight%289%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=3x%5E2-12x%2Bhighlight%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) Correct!<BR>\n" );
document.write( "c) Correct!<BR>\n" );
document.write( "d) Correct!<BR>\n" );
document.write( "e)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=3%2Asinh%28x%29%2B4%2Asinh%28x%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=3%2Asinh%28x%29%2B4%2Asinh%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I think you misinterpreted as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28hx%29 ALIGN=MIDDLE  ALT=\"sin%28hx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > when it's actually the hyperbolic sine function, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sinh%28x%29 ALIGN=MIDDLE  ALT=\"sinh%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, same for the cosine.<BR>\n" );
document.write( "f)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%28x%5E2%2B1%29cosh%28x%29%2B%282x%29sinh%28x%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=%28x%5E2%2B1%29cosh%28x%29%2B%282x%29sinh%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "2a) Correct! Could be simplified to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=e%5Ex%28x%2B2%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=e%5Ex%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "b) Correct!<BR>\n" );
document.write( "c) Correct! Could be simplified to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=4x%5E3%28ln%28x%29%2B1%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=4x%5E3%28ln%28x%29%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d) Correct!<BR>\n" );
document.write( "e) Correct! Could be simplified to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=-e%5E%28-x%29%28cos%28x%29+%2Bsin%28x%29%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=-e%5E%28-x%29%28cos%28x%29+%2Bsin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "f) Correct! but why weren't your answers for 1f and 2f the same??<BR>\n" );
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document.write( "3a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%281%2Be%5E%28-x%29%29cos%28x%29-sin%28x%29%28-e%5E%28-x%29%29%2F%281%2Be%5E%28-x%29%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%28%281%2Be%5E%28-x%29%29cos%28x%29%2Be%5E%28-x%29sin%28x%29%29%2F%281%2Be%5E%28-x%29%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=+%28%281%2Bx%5E2%29%281%2Fx%29-ln%28x%29%282x%29%29%2F%281%2Bx%5E2%29%5E2 ALIGN=MIDDLE  ALT=\"dy%2Fdx=+%28%281%2Bx%5E2%29%281%2Fx%29-ln%28x%29%282x%29%29%2F%281%2Bx%5E2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=+%28%281%2Bx%5E2%29-2x%5E2ln%28x%29%29%2F%28x%281%2Bx%5E2%29%5E2%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=+%28%281%2Bx%5E2%29-2x%5E2ln%28x%29%29%2F%28x%281%2Bx%5E2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%28x%5E2-2x%5E2ln%28x%29%2B1%29%2F%28x%28x%5E2%2B1%29%5E2%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=%28x%5E2-2x%5E2ln%28x%29%2B1%29%2F%28x%28x%5E2%2B1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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