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Math Help - Implicit differentiation

  1. #1
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    Implicit differentiation

    Hello

    sin(2x^3 + y^2) = cos(x^2 + 2y^3)

    How would this be solved using implicit differentiation?

    Thank you
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  2. #2
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    I'll do the left hand side and let you do the right.

    \cos(2x^3+y^2) (6x^2+2y*y') = ...

    Use the chain rule. The outermost function in this case was the sine function, then multiply by the derivative of the inner terms. Same thing for the right hand side.

    Then, you'll have to do some algebra to solve for y'.
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  3. #3
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    I see. How would you express the derivative of cos(u) using the chain rule when u = 2x^3 + y^2?

    Thank you
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  4. #4
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    u' = 6x^2 + 2y'y

    -sin(2x^3 + y^2) (6x^2 + 2y'y)

    Should be like that
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  5. #5
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    Thank you. How would this application of the chain rule be written in the form: dy/dx = du/dx * ..., for example?
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