If x=8, then y=8, and the tangent line passing through the point (8, 8) has slope -1. Substitue this into the ORIGINAL equation Since lines tangent to the graph will have slope $ -1 $, set y' = -1, getting Differentiate both sides of the equation, getting Use Equation 2 to substitute into the equation for y'', gettingĪnd the second derivative as a function of x and y isĬlick HERE to return to the list of problems. This answer can be simplified even further. (Get a common denominator in the numerator and simplify the expression.) Use Equation 1 to substitute for y', getting To find y'', differentiate both sides of this equation, getting Differentiate both sides of the equation, gettingĪnd the first derivative as a function of x and y is SOLUTIONS TO IMPLICIT DIFFERENTIATION PROBLEMS Solutions to Implicit Differentiation Problems
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