text: I assume that you meant for 7xeY + 3x^3 = 5y^4 to mean 7xe^y + 3x^3 = 5y^4.\n\nWe now take dy/dx of both sides:\nD(7x)e^y + D(e^y)7x + D(3x^3) = D(5y^4).  D refers to the derivative.  \nThus we get 7e^y + 7xe^yy' + 9x^2 = 20y^3y'.  \nSimplify this to be 7e^y + 9x^2 = 20y^3y' - 7xe^yy' .  \nNow factor out the y': 7e^y + 9x^2 = y'(20y^3 - 7xe^y).  \n\nSolve for y': The final answer is (7e^y + 9x^2)/(20y^3 - 7xe^y). This is choice d. \n\nMake sure to use proper parentheses.