1. CHAPTER 2 2.4 Continuity Implicit Differentiation

2. CHAPTER 2 2.4 Continuity Example Find dx / dy by implicit differentiation for x 2 + y 2 = 36. 1. Differentiate both sides of the equation with respect to the independent variable. 2. Solve, if possible, the equation for the derivative of the independent variable.

3. CHAPTER 2 2.4 Continuity Example Find y’ if : x sin y + cos2y = cos y.

4. CHAPTER 2 2.4 Continuity Example Find an equation of the tangent line of the ellipse equation (x 2 /9) + (y 2 /36) = 1 at the point (-1, 4  2).

5. Derivatives of Inverse Trigonometric Functions d / dx (sin –1 x) = 1 / (  1 – x 2 ) d / dx (tan –1 x) = 1 / (1 + x 2 ) The derivative of the arcsine function: The derivative of the arctangent function:

6. CHAPTER 2 2.4 Continuity Example Differentiate f (t) = x arcsin ( 1 - x 2 ).