How do you differentiate #f (x) = 3 arcsin (x^4)#?

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Answer 1 · 2018-03-31T15:17:01

#dy/dx=(12x^3)/sqrt(1-x^8)#

#f(x)=3arcsin(x^4)#

Let
#y=f(x)#

#3arcsin(x^4)=3sin^-1(x^4)#

#y=3sin^-1(x^4)#

Let #u=x^4#

#y=3sin^-1u#

#dy/dx=dy/(du).(du)/dx#

#y=3sin^-1u#

#dy/(du)=3xx1/sqrt(1-u^2)#

#u=x^4#

#u^2=(x^4)^2#
#u^2=x^8#

#dy/(du)=3/sqrt(1-x^8)#

#u=x^4#

#(du)/dx=4x^3#

#dy/dx=dy/(du).(du)/dx#

#dy/dx=(3/sqrt(1-x^8)).(4x^3)#

#dy/dx=(12x^3)/sqrt(1-x^8)#