document.write( "Question 376103: Hi can somebody please help with the below, and be as kind as to talk me through the steps, i am totally confused with this. \r
\n" ); document.write( "\n" ); document.write( "Find dy=dx as a function of x and y when:\r
\n" ); document.write( "\n" ); document.write( "i) x^2y^3 - x^2 + 3y - 3 = 0
\n" ); document.write( "ii)(1 - x^2) tan^-1 y = 3\r
\n" ); document.write( "\n" ); document.write( "Really appreciate this.\r
\n" ); document.write( "\n" ); document.write( "Thanks
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #267603 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
Find dy/dx as a function of x and y when:
\n" ); document.write( "i) x^2y^3 - x^2 + 3y - 3 = 0
\n" ); document.write( "Differentiate implicitly
\n" ); document.write( "2x*dx*y^3 +x^2*3y^2*dy - 2xdx + 3dy = 0
\n" ); document.write( "dx*(2xy^3 - 2x) + dy*(x^2*3y^2 + 3) = 0
\n" ); document.write( "dy*(3x^2y^2 + 3) = -dx(2xy^3 - 2x)
\n" ); document.write( "dy/dx = -2(xy^3 - x)/(3x^2y^2 + 3)
\n" ); document.write( "------------------------------------
\n" ); document.write( "ii)(1 - x^2) tan^-1 y = 3
\n" ); document.write( "Use atan for arctan, easier to type
\n" ); document.write( "atan(y) - x^2*atan(y) = 3
\n" ); document.write( "dy/(1+y^2) - (2x*dx*atan(y) + x^2*dy/(1+y^2) = 0
\n" ); document.write( "Multiply thru by (1+y^2)
\n" ); document.write( "dy - 2x*dx*atan(y)*(1+y^2) - x^2*dy = 0
\n" ); document.write( "(1-x^2)dy = 2x*atan(y)*(1+y^2)dx
\n" ); document.write( "dy/dx = 2x*atan(y)*(1+y^2)/(1-x^2) with y <> ± 1
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