For the curve xy(x+y)=84, find dy/dx at (3,4)

Implicit differentiation, yeah

hmm, never seen derivitive of 3 of them before

let's distribute

x²y+xy²=84
implicit differntiation

remember, dy/dx f(x)g(x)=f'(x)g(x)+f(x)g'(x)
and dy/dx y=dy/dx

so
2xy+x² dy/dx+y²+2xy dy/dx=0
solving for dy/dx
minus (2xy+y²) from both sides
x² dy/dx +2xy dy/dx=-2xy-y²
undistribute dy/dx
dy/dx(x²+2xy)=-2xy-y²
divide both sides by (x²+2xy)


at (3,4)
evalaute for x=3 and y=4

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.