To find the derivative of the function f(x) = 4sin^-1(x^4) and then evaluate it at x = 0.7, we need to apply the chain rule and the power rule for differentiation.
First, let's find the derivative of f(x):
f'(x) = 4*(d/dx)[sin^-1(x^4)]
To differentiate sin^-1(x^4), we can rewrite it as arcsin(x^4) and apply the chain rule:
f'(x) = 4 * (1/sqrt(1 - (x^4)^2)) * (d/dx)(x^4)
= 4 * (1/sqrt(1 - x^8)) * 4x^3
= 16x^3 / sqrt(1 - x^8)
Now, let's evaluate f'(x) at x = 0.7:
f'(0.7) = 16*(0.7)^3 / sqrt(1 - (0.7)^8)
Using a calculator, we can calculate the numerical value of f'(0.7).
Please note that the derivative and evaluation of f'(x) at x = 0.7 is a numerical calculation that may require a calculator or software for accurate results.