Implicit Differentiation: Finding d^2y/dx^2 at a Given Point

[athamz]

Homework Statement

find the d^2y/dx^2 if y^3 + y = 2 cos x at the point (0,1)

Homework Equations

The Attempt at a Solution

my dy/dx = (-2 sin x)/(3y^2 + 1)

I don't know how to find d^2y/dx^2?
And when and how will I use the oint (0,1)?

 

[ehild]

Differentiate both sides of the equation twice with respect to x, using chain rule on the left-hand size (differentiate with respect to y first than with respect to x).

ehild

 

[athamz]

oh.. so I have..

3y^2 * y' + y' = -2 sin x

y'(3y^2 + 1) = -2 sin x

y' = (-2 sin x)/(3y^2 + 1)

Right?

 

[ehild]

It is right. Get the second differential. But differentiate both sides of the equation y'(3y^2 + 1) = -2 sin x instead of the last one. It will be an easier process.

ehild