y for y = \\sqrt3{(8x - 3)(x - 5)(7x + 2)}

Explanation:

Step1: Take natural - log of both sides

$\ln y=\frac{1}{3}[\ln(8x - 3)+\ln(x - 5)+\ln(7x + 2)]$

Step2: Differentiate both sides

$\frac{y'}{y}=\frac{1}{3}(\frac{8}{8x - 3}+\frac{1}{x - 5}+\frac{7}{7x + 2})$

Step3: Solve for $y'$

$y'=\frac{1}{3}\sqrt[3]{(8x - 3)(x - 5)(7x + 2)}(\frac{8}{8x - 3}+\frac{1}{x - 5}+\frac{7}{7x + 2})$

Answer:

$y'=\frac{1}{3}\sqrt[3]{(8x - 3)(x - 5)(7x + 2)}(\frac{8}{8x - 3}+\frac{1}{x - 5}+\frac{7}{7x + 2})$