# Thread: Slope of a tangent through implicit differentitation

1. ## Slope of a tangent through implicit differentitation

i have a problem where I have to find tangent line to the curve: 1x2–4xy+4y3=81
At the point (–71).
Can anyone help?

2. Originally Posted by quitie0690
i have a problem where I have to find tangent line to the curve: 1x2–4xy+4y3=81
At the point (–71).
Can anyone help?
Is the equation $x^2 - 4xy + 4y^3 = 81$ ? Have you learned implicit differentiation?

3. Yes that's the line. Sorry about that. Well, let's just say my prof. isn't the best in the world (aka the world's biggest understatement). We've only done a few examples. but I can't figure this one out. Can you help?

4. Originally Posted by mr fantastic
Is the equation $x^2 - 4xy + 4y^3 = 81$ ? Have you learned implicit differentiation?
Originally Posted by quitie0690
Yes that's the line. Sorry about that. Well, let's just say my prof. isn't the best in the world (aka the world's biggest understatement). We've only done a few examples. but I can't figure this one out. Can you help?
Differentiate both sides with rspect to x:

Use the product rule on 4xy to get $4y + 4x \frac{dy}{dx}$.

Use the chain rule on $4 y^3$ to get $12 y^2 \frac{dy}{dx}$.

Now substitute (-7, 1) and make $\frac{dy}{dx}$ the subject.