1. Tardigrade
  2. Question
  3. Mathematics
  4. If y=(x-1)2(x-2)3(x-3)5 then (d y/d x) at x=4 is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

KCETKCET 2021Continuity and Differentiability

Solution:

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