How do you differentiate y= 2 sin ^-1 (4x^4)?

1 Answer
May 6, 2017

Use the chain rule:

When given: y= f(g(x))

dy/dx = (df(g))/(dg)(dg)/dx

Explanation:

Let g(x)= 4x^4 and f(g) = 2sin^-1(g), then:

(df(g))/(dg) = 2/sqrt(1-g^2)

(dg)/dx = 16x^3

Substitute into the chain rule:

dy/dx = (2/sqrt(1-g^2))16x^3

Reverse the substitution for g:

dy/dx = (32x^3)/sqrt(1-16x^8)