Question

If $y=(x-1{)}^2(x-2{)}^3(x-3{)}^5$ then $\frac{dy}{dx}$ at $x=4$ is equal to

• A. 108
• B. 54
• C. 36
• D. 516

Answer 1

Answer: (D)

$\log y=2\log (x-1)+3\log (x-2)+5\log (x-3)$
$\frac{dy}{dx}=(x-1{)}^2(x-2{)}^2(x-3{)}^5\left[\frac{2}{x-1}+\frac{3}{x-2}+\frac{5}{x-3}\right]$
${\left(\frac{dy}{dx}\right)}_{x=4}=516$