Section 3.5 Implicit Differentiation We know what we are, but know not what we may be. - William Shakespeare

Find the slope of the tangent line at the point P

Find the slope of the tangent line at the point P

Find the slope of the tangent line at the point P

Any graph of a relationship between x and y can be considered a combination of functions. Y is defined implicitly by as several functions of x. We can use a single variable or f(x) notation to represent all these functions. As we differentiate with respect to x, we must acknowledge the effect x is having on all of these functions. In other words, for each term containing a “y” in our original relationship, we must have a derivative of y explicitly mentioned in our implicit derivative.

Find if

Find if

Find if

Find if

Derivatives of Inverse Trigonometric Functions