Class 12

Math

Calculus

Application of Derivatives

A balloon, which always remains spherical, has a variable diameter $23 (2x+1)$.Find the rate of change of its volume with respect to x.

$ddxv =?,v=34 πx_{3}=6π d_{3}$

$dxd(6π )d_{3} =6π dxd(d_{3}) $

$=6π dd(d_{3}) dxd(d) $

$=63π d_{2}dxd(23 )(2x+1) $

$=(2π 23 d_{2})dxd2x+1 $

$=(43πd_{2} )2$

$=23π d_{2}$

$=23 π(23 (2x+1))_{2}$