If `y=(2x+3)^((3x-5))`, find `(dy)/(dx)`.

1.	If `y=(2x+3)^((3x-5))`, find `(dy)/(dx)`.
Answer» Given: `y=(2x+3)^((3x-5))." …(i)"` Taking logarithm on both sides of (i), we get `log y = (3x-5)log(2x+3)." …(ii)"` On differentiating both sides of (ii) w.r.t. x, we get `(1)/(y).(dy)/(dx)=(3x-5).(d)/(dx){log(2x+3)}+log(2x+3).(d)/(dx)(3x-5)` `=(3x-5).(1)/((2x+3)).2+log(2x+3).3` `rArr(dy)/(dx)=y.{((6x-10))/((2x+3))+3log(2x+3)}` `rArr(dy)/(dx)=(2x+3)^((3x-5)).{((6x-10))/((2x+3))+3log(2x+3)}.`

Discussion

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