differentiate the function y = in (6x² - 3x + 4). choose the correct setup below to start differentiating…

differentiate the function y = in (6x² - 3x + 4). choose the correct setup below to start differentiating the function. a. y = d/dx in (6x²) - d/dx in (3x) + d/dx in 4 b. y = 1/(6x² - 3x + 4) · d/dx 6x² - 3x + 4 c. y = (6x² - 3x + 4) · d/dx 6x² - 3x + 4 d. y = 1/d/dx 6x² - 3x + 4 y =

differentiate the function y = in (6x² - 3x + 4). choose the correct setup below to start differentiating the function. a. y = d/dx in (6x²) - d/dx in (3x) + d/dx in 4 b. y = 1/(6x² - 3x + 4) · d/dx 6x² - 3x + 4 c. y = (6x² - 3x + 4) · d/dx 6x² - 3x + 4 d. y = 1/d/dx 6x² - 3x + 4 y =

Answer

Explanation:

Step1: Recall chain - rule for $\ln(u)$

If $y = \ln(u)$, then $y'=\frac{1}{u}\cdot u'$. Here $u = 6x^{2}-3x + 4$.

Step2: Differentiate $u = 6x^{2}-3x + 4$

Using the power - rule $\frac{d}{dx}(ax^{n})=nax^{n - 1}$, we have $\frac{d}{dx}(6x^{2}-3x + 4)=12x-3$.

Step3: Find $y'$

$y'=\frac{1}{6x^{2}-3x + 4}\cdot(12x - 3)=\frac{12x-3}{6x^{2}-3x + 4}$.

Answer:

$\frac{12x - 3}{6x^{2}-3x + 4}$