Ms. Battaglia AB/BC Calculus

Up to this point, most functions have been expressed in explicit form. Ex: y=3x 2 – 5 The variable y is explicitly written as a function of x. How would you find dy/dx for x 2 – 2y 3 + 4y = 2? You can use implicit differentiation (apply the Chain Rule, because you are assuming that y is defined implicitly as a differentiable function of x). Implicit FormExplicit FormDerivative

Variables agree Variables disagree 

1. Differentiate both sides of the equation with respect to x. 2. Collect all terms involving dy/dx on the left side of the equation and move all other terms to the right side of the equation. 3. Factor dy/dx out of the left side of the equation. 4. Solve for dy/dx.

Find dy/dx given that y 3 + y 2 – 5y – x 2 = -4

If possible, represent y as a differentiable function of x. a. x 2 + y 2 = 0 b. x 2 + y 2 = 1c. x + y 2 = 1

Determine the slope of the tangent line to the graph of x 2 + 4y 2 = 4 at the point

Determine the slope of the graph of 3(x 2 + y 2 ) 2 = 100xy at the point (3,1).

Find dy/dx implicitly for the equation siny=x

Given x 2 + y 2 = 25, find. Evaluate the 1 st and 2 nd derivatives at the point (-3,4).

Find the tangent line to the graph given by x 2 (x 2 + y 2 ) = y 2 at the point.

 Read 2.5, Page 146 #7, 11, 21, 27, 30, 45, 47, 51