Differentiation

Question

Differentiate with respect to x.

 ln[ (x+3)³ cos3x / sin x ]

 

Thank You ! :)

 

Ans : 3/(x+2) -3tan3x -cotx

Answer 1

The given answer is wrong.

 

The solution is as follows-----

 

taking derivative of the given function---

 

[Sin(x)/[((x+3)^3)cos(3x)]]*[sin(x)[3((x+3)^2)*cos3x-3*((x+3)^3)*sin(3x)]-((x+3)^3)*cos(3x)*cos(x)]/(sin(x)^2)

 

Simplifying----

 

[1/sin(x)*cos(3x)*((x+3)^3)]*[3sin(x)*cos(3x)*((x+3)^2)-3sin(x)*sin(3x)*((x+3)^3)-cos(x)*cos(3x)*(x+3)^3]

 

on further simplifying

 

[(3/(x+3))-3tan(3x)-cot(x)]