document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167547>Question 167547</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello all! I have this Trigonometry homework that is killing me and I need help from you guy's. Here's the problem let me know if you guys can solve it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1. Calculate the derivatives:\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "I)                   I) (Sin4x) /( x² +1)\r<BR>\n" );
document.write( "\n" );
document.write( "II)                 II) 10t²+1\r<BR>\n" );
document.write( "\n" );
document.write( "III)              III) &#8730; ( 1 + u) / (1 – u)\r<BR>\n" );
document.write( "\n" );
document.write( "IV)              IV) (1) / ( x­­­­­­­4 + 1)3\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "2.  Calculate the points of the tangent of the curve  : y = ex(x2 – 8) where and in which the tangent line is horizontal\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "3. Write one of the two tangents to the curve : y = 1 + x³   which are parallel to this equation 12x - y = 1.\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "4.  Calculate\r<BR>\n" );
document.write( "\n" );
document.write( "I) If  f(x) = ex cos x calculate f ’(x) et f ’’\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "(ii) Calculate (d99/ dx99) Sin x\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "5.\r<BR>\n" );
document.write( "\n" );
document.write( "Calculate the derivative :\r<BR>\n" );
document.write( "\n" );
document.write( " I) y = xe-x²\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "II) Let say:  r(x) = f(g(h(x))) whit h(1) = 2, g(2) = 3, h’(1)= 4, g’(2) = 5, f’(3) = 6. Calculate r’(1).\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "III) Show that the function : y = Ae-x + Be-x satisfy the equation with differential y”+ 2y’+y = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123445 by </B><A HREF=/tutors/aboutme.mpl?userid=sowmya><B>sowmya(32)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sowmya><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.Derivatives:\r<BR>\n" );
document.write( "\n" );
document.write( "i)(Sin4x) /( x² +1)<BR>\n" );
document.write( "Let y = (sin4x)/x^2 +1<BR>\n" );
document.write( "    dy/dx use u/v method<BR>\n" );
document.write( "d(u/v) = (vdu-udv)/v^2\r<BR>\n" );
document.write( "\n" );
document.write( "Here , u = sin4x<BR>\n" );
document.write( "v= x^2 +1<BR>\n" );
document.write( "du = 4 cos4x<BR>\n" );
document.write( "dv = 2x\r<BR>\n" );
document.write( "\n" );
document.write( "dy/dx = ((x^2 +1)4cos4x- sin4x(2x))/(x^2 +1)^2<BR>\n" );
document.write( "      = (4x^2 cos4x + 4 cos4x - 2x sin4x)/(x^2+1)^2\r<BR>\n" );
document.write( "\n" );
document.write( "ii)10t^2 +1<BR>\n" );
document.write( "y = 10 t^2 +1<BR>\n" );
document.write( "dy/dt = 20 t \r<BR>\n" );
document.write( "\n" );
document.write( "iii)y= sqrt((1+u)/(1-u))\r<BR>\n" );
document.write( "\n" );
document.write( "y^2 = (1+u)/1-u)\r<BR>\n" );
document.write( "\n" );
document.write( "2y dy = ((1-u) du + (1+u) du)/(1-u)^2<BR>\n" );
document.write( " 2y dy = 2du/(1-u)^2\r<BR>\n" );
document.write( "\n" );
document.write( "y dy = du/(1-u)^2\r<BR>\n" );
document.write( "\n" );
document.write( "dy/du = y/(1-u)^2<BR>\n" );
document.write( "         = sqrt((1-u)(1+u))/(1-u)^2<BR>\n" );
document.write( "        = (sqrt(1+u))/(1+u)^3/2\r<BR>\n" );
document.write( "\n" );
document.write( "iv)question not clear\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );