Differentiate (2x−3)(x⎯⎯√+1)x⎯⎯√ with respect to x.

To differentiate the function \((2x - 3)(\sqrt{x} + 1)\sqrt{x}\) with respect to \(x\), we'll need to apply both the product rule and the chain rule. Let's break it down step by step.

Given:
\[ f(x) = (2x - 3)(\sqrt{x} + 1)\sqrt{x} \]

First, simplify the expression if possible:
\[ f(x) = (2x - 3)(\sqrt{x} + 1)x^{1/2} \]

Let's denote:
\[ u = 2x - 3 \]
\[ v = (\sqrt{x} + 1)x^{1/2} \]

Now, differentiate \(u\) and \(v\) with respect to \(

Learn how to differentiate the function (2x−3)(√x+1)x√x with respect to x using the product rule and chain rule. This problem involves advanced differentiation techniques and the manipulation of square root functions.

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