Okay, Now, if we simplify everything that we see here, um, we're gonna have why? Prime? Yeah, is equal to three. And then the derivative of everything in those parentheses is to X plus two. And then, if you decker Ament, that's gonna be too the 1/2 power. So that derivative is three halves times x squared, plus two X. All of that's gonna be multiplied by the natural log of three, okay, and Then you figure out what is the derivative of this expression you see right here. So I'm gonna have X squared plus two x to the three halves power. So, in order to find the derivative we have here, why prime it's going to be equal to so here My f of X is this X squared plus two extra the three halves. Why, prime, it's going to be f prime of X over f of x times the natural log of three. If y is equal to the log, must pick based three of half of axe. Do we know that why prime is gonna be one over x times the natural log of three extending that with a chain rule. So what is guiding us here? Remember, if wise equal to the log, let's pick based three of X. So why is the long based three of X square plus two x x squared plus two x raised to the three halves power. Section 4.5 Everything here dealing with functions that have logarithms and their derivatives.
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