# Math Help - implicit differentiation

1. ## implicit differentiation

I'm having trouble with this problem. I keep thinking I'm doing it right, but when I plug it in I'm wrong. Someone please help.

2. x^2-3xy-2y^3=-148

I need to find the slope of the tangent line to the curve at (2,4)

Whelp, due date passed, thanks.

2. Originally Posted by nobodygirl
I'm having trouble with this problem. I keep thinking I'm doing it right, but when I plug it in I'm wrong. Someone please help.

2. x^2-3xy-2y^3=-148

I need to find the slope of the tangent line to the curve at (2,4)

Whelp, due date passed, thanks.
Differentiating with respect to x we have:

$
\frac{d}{dx}[x^2-3xy-2y^3]=0
$

$
2x - 3\left[x \frac{dy}{dx}+y\right]-6y^2\frac{dy}{dx}=0
$

So collecting the terms with the derivative and rearranging gives:

$
(3x+6y)\frac{dy}{dx}=2x-3y
$

or:

$
\frac{dy}{dx}=\frac{2x-3y}{3(x+2y^2)}=\frac{2\times 2-3 \times 4}{3(2+2\times 16)}=\frac{4}{51}
$

RonL