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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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#### Solution Preview

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.

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