document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993255>Question 993255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose ln (x + 2y) = x^4.\r<BR>\n" );
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document.write( "Use implicit differentiation to find the derivative of y with respect to x\r<BR>\n" );
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document.write( "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 #612553 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=612553\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> d/dy(ln(x+2y))= d/dy(x^4)<BR>\n" );
document.write( "Chain rule: d/dy(log(x+2y)) = (dlog(u))/(du)(du)/(dy), where u= x+2y and (d)/(du)(log(u))= 1/u:<BR>\n" );
document.write( "(d/dy(x+2y))/(x+2y)= d/dy(x^4)<BR>\n" );
document.write( "Differentiate the sum term by term and factor out constants:<BR>\n" );
document.write( "d/dy(x)+2d/dy(y)/(x+2y)= d/dy(x^4)<BR>\n" );
document.write( "The derivative of x is zero:<BR>\n" );
document.write( "(2(d/dy(y))+0)/(x+2 y)= d/dy(x^4)<BR>\n" );
document.write( "Simplify the expression:<BR>\n" );
document.write( "(2(d/dy(y)))/(x+2y)= d/dy(x^4)<BR>\n" );
document.write( "The derivative of y is 1:<BR>\n" );
document.write( "((1)(2))/(x+2 y)= d/dy(x^4)<BR>\n" );
document.write( "The derivative of x^4 is zero:<BR>\n" );
document.write( "2/(x+2 y)= 0 </SPAN>\n" );
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