MATH 151 SI Name 6.4-β6.5 6.4 Implicit Differentiation How to find dy/dx implicitly? 1. Take the derivative of the function: Example π¦ ln π₯ + 4π₯ = 13π¦ Derivative aaa All normal rules apply (power, product, ! quotient, exponential, log, chain) β’ Did you take the derivative of y? Multiply by dy/dx o Did you take the derivative of x? β’ Leave this as is (or multiply by o dx/dx=1) 2. Move all terms with a dy/dx in them to one side of the equation and all terms without dy/dx to the other side β’ You may need to expand or get rid of your fractions 3. Factor out dy/dx and solve for dy/dx 2π¦ ln π₯ β + !! ! + 4 = 13 β !" !" ππ¦ π¦ ! ππ¦ + + 4 = 13 β ππ₯ π₯ ππ₯ π¦! ππ¦ ππ¦ + 4 = 13 β β 2π¦ ln π₯ β π₯ ππ₯ ππ₯ by dividing by what is left !" You took the derivative of y so multiply by dy/dx 2π¦ ln π₯ β !" π¦! ππ¦ +4= (13 β 2π¦ ln π₯) π₯ ππ₯ ππ¦ π¦! 4 = + ππ₯ π₯ 13 β 2π¦ ln π₯ 13 β 2π¦ ln π₯
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