Let $h(x) = f(x)g(x)$. If $f(x) = 4x^2 - 3x$ and $g(x) = \ln(3x - 1)$, what is $h'(x)$? Select the correct answer below. $h'(x) = (3 - 8x) \ln(3x - 1) + \frac{12x^2 - 9x}{1 - 3x}$ $h'(x) = (8x - 3)(3x - 1) + \frac{12x^2 - 9x}{3x - 1}$ $h'(x) = (8x - 3) \ln(3x - 1) + \frac{4x^2 - 3x}{3x - 1}$ $h'(x) = (8x - 3) \ln(3x - 1) + \frac{12x^2 - 9x}{3x - 1}$ $h'(x) = (8x - 3) \ln(3x - 1) - \frac{12x^2 - 9x}{3x - 1}$
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We will use the product rule for differentiation, which states that if $h(x) = f(x)g(x)$, then $h'(x) = f'(x)g(x) + f(x)g'(x)$. Show more…
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