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

1 Answer
Mar 31, 2018

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

Explanation:

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

By chain rule

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)