How do you differentiate #f(x)=sqrt(sin(1/(x-2)^2)# using the chain rule?

1 Answer
Apr 10, 2018

Answer:

#I=-1/(x-3)^3xxcos(1/(x-2)^2)/sqrtsin(1/(x-2)^2)#

Explanation:

Here,

#f(x)=sqrt(sin(1/((x-2)^2))#

#"Using "color(blue) "Chain Rule"#

#f'(x)=1/(2sqrtsin(1/(x-2)^2))d/(dx)(sin(1/(x-2)^2))#

#=1/(2sqrtsin(1/(x-2)^2))xxcos(1/(x-2)^2)d/(dx)((x-2)^-2)#

#=1/(cancel2sqrtsin(1/(x-2)^2))xxcos(1/(x-2)^2)[-cancel2(x- 2)^-3]#

#=-1/(x-3)^3xxcos(1/(x-2)^2)/sqrtsin(1/(x-2)^2)#