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
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
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:
10. (a) Use implicit differentiation to find an equation of the tangent line ...
It shows how to find the derivative and equation of tangent line by implicit differentiation.