Use implicit differentiation to determine y' if y = e^(3x + 18)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function `y = e^(3x + 18)` . The derivative y' has to be determined using implicit differentiation.

`y = e^(3x + 18)`

Take the natural logarithm of both the sides

=> `ln y = 3x + 18`

Using implicit differentiation

`y'*(1/y) = 3`

=> `y' = y*3`

=> `y' = 3*e^(3x + 18)`

The derivative `y' = 3*e^(3x + 18)`

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