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    Implicit differentiation, equation of the tangent line

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    Please see the attached problem for the full questions.

    1) Find f'(x) and f'(c): f(x) = x^2 - 4 / x - 3, c =1
    2) Find dy/dx by implicit differentiation: sinx + 2cos2y = 1

    3)
    A) Use implicit differentiation to find an equation of the tangent line to the ellipse:
    x^2/2 + y^2/8 = 1 at (1,2)

    B) Show that the equation of the tangent line to the ellipse 2^2/a^2 + y^2/b^2 = 1 at (x_0,y_0) is
    x_0 x/ a^2 + y_0 y/b2^2 = 1

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    https://brainmass.com/math/derivatives/implicit-differentiation-equation-tangent-line-493852

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    6. Find and :
    Applying the quotient rule and chain rule

    Then substitute 1 for x to find out f'(x=1)

    9. Find by implicit differentiation:
    Applying chain rule, and differentiating on both sides of equation:

    So

    10. (a) Use implicit differentiation to find an equation of the tangent line ...

    Solution Summary

    It shows how to find the derivative and equation of tangent line by implicit differentiation.

    $2.49

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