Implicit differentiation

  • Thread starter athamz
  • Start date
  • #1
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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)?
 

Answers and Replies

  • #2
ehild
Homework Helper
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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
 
  • #3
11
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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?
 
  • #4
ehild
Homework Helper
15,543
1,912
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
 

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