text: wrong question, here is the right question? use implicit differentiation to determine  dy / dx for 7xey + 3x^3 = 5y^4 show work. here are the choices  (a) dy / dx = 7xey + 9x^2 / 20y^3 - 7ey  (b) dy /dx = 7ey + 9x^2 / 20y^3 + 7xey  (c) dy /dx = 7xey - 9x^2 / 20y^3 + 7ey  (d) dy /dx = 7ey + 9x^2 / 20y^3 - 7xey i assume that you meant for 7xey + 3x^3 = 5y^4 to mean 7xe^y + 3x^3 = 5y^4.  we now take dy/dx of both sides: d(7x)e^y + d(e^y)7x + d(3x^3) = d(5y^4).  d refers to the derivative.   thus we get 7e^y + 7xe^yy' + 9x^2 = 20y^3y'.   simplify this to be 7e^y + 9x^2 = 20y^3y' - 7xe^yy' .   now factor out the y': 7e^y + 9x^2 = y'(20y^3 - 7xe^y).    solve for y': the final answer is (7e^y + 9x^2)/(20y^3 - 7xe^y). this is choice d.   make sure to use proper parentheses.