Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2 - Page 425: 15

$2x\log_2(3-2x)-\frac{2x^2}{(\ln 2)(3-2x)}$

$\frac{d}{dx}x^2\log_2(3-2x)$ $=x^2\frac{d}{dx}\log_2(3-2x)+\log_2(3-2x)\frac{d}{dx}x^2$ $=x^2\frac{1}{(3-2x)\ln 2}\frac{d}{dx}(3-2x)+\log_2(3-2x)*2x$ $=x^2\frac{1}{(3-2x)\ln 2}*-2+\log_2(3-2x)*2x$ $=2x\log_2(3-2x)-\frac{2x^2}{(\ln 2)(3-2x)}$