Find dy/dx if 3xy = 4x + y^2

Re: dy/dx

What do you know about implicit differentiation?.
 
Re: dy/dx

\(\displaystyle 3xy-4x-y^{2}=0\)

Use the product rule on xy. That is something often overlooked by 'rookie' implicit differentiators :D .

\(\displaystyle 3(xy'+y)-4-2yy'=0\)

Solve for y'.
 
calculusqueen said:
Find dy/dx if 3xy = 4x + y^2
Click to expand...

Avoiding implicit differentiation:

y[sup:1nhzayms]2[/sup:1nhzayms] - 3xy + 4x = 0 <<< Use quadratic formula

y = [3x ± ?(9x[sup:1nhzayms]2[/sup:1nhzayms] - 16x)]/2 <<< Now differentiate

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