1. Consider the following equation.

Question

xy + 7x + 5y = –8

(a) Differentiate both sides with respect to x to complete the following.

( blank )y ' + y + blank =0

(b)Solve for y ' in terms of x and y.

(c) Calculate dy/dx at the point (4,-4).

Can anyone help me on this questions I'm struggling so badly....

Answer 1

for xy + 7x + 5y = –8
use the product rule for the xy term

x(dy/dx) + y + 7 5dy/dx = 0
dy/dx(x+5) = -y-7
dy/dx = -(y+7)/(x+5)
sub in the point (4,-4)

Answer 2

which one is part a and part b.