CHAPTER Continuity Implicit Differentiation

CHAPTER Continuity Example Find dx / dy by implicit differentiation for x 2 + y 2 = 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.

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

CHAPTER 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).

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:

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