Posted by **Karen** on Saturday, December 20, 2008 at 5:03pm.

Find dy/dx for: 2y^3 - 3xy = 4

Write an equasion for the line tangent to the curve at (1,2)

Find d^2y/dx^2 at (1,2)

- Calculus -
**drwls**, Saturday, December 20, 2008 at 7:21pm
As you can see, it is not easy to solve for y in terms of x only and then differentiate that equation. It is much easier to use the method called "implicit differentiation" in which you take the derivative of both sides of the equation, treating y as a function of x. This results in:

6y^2*dy/dx - 3x*dy/dx -3y = 0

dy/dx*(2y^2-x) = y

dy/dx = y/(2y^2-x)

At (1,2), dy/dx = 2/(8-1) = 2/7

Use that slope and the coordinates (1,2) that the line must pass through to get the equation of the tangent line.

For the second derivative, differentiate an equation containing dy/dx impliticly with respect to x.

dy/dx*(2y^2-x) = y

d^2y/dx^2*(2y^2-x)

+ dy/dx (4y*dy/dx -1) = dy/dx

Insert the value of dy/dx = 2/7 that you already know at the point (1,2), and solve for d^2y/dx^2 at the same point.

- Calculus -
**Karen**, Tuesday, December 30, 2008 at 7:04pm
I did that and got 2... my friend said the answer is just 2/7. Is she right?

## Answer this Question

## Related Questions

- Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...
- Calculus - 2y^3 - 3xy = 4 1) Find dy/dx 2) Write an equation for the line ...
- Calculus - Find the equation of the tangent line to the curve x^(3)+3xy+y^(3)=1 ...
- Calculus AP - implicit differentiation Find the slope of the tangent line to ...
- Calculus AP need help! - i dont know how or what to starts Find the slope of the...
- calculus - Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show ...
- Calculus - the curve: (x)(y^2)-(x^3)(y)=6 (dy/dx)=(3(x^2)y-(y^2))/(2xy-(x^3)) a...
- Calculus - If F(x)=x^3−7x+5, use the limit definition of the derivative to...
- AP AB Calculus - Linear approximation: Consider the curve defined by -8x^2 + 5xy...
- AP Calculus - Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y-...