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

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Answer 1 · 2017-05-06T17:14:01

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

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

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)#