How do you find derivative of f(x) = 3 arcsin (x^4)f(x)=3arcsin(x4)?

1 Answer
Bill K.
Aug 13, 2015

f'(x)=(12x^3)/sqrt{1-x^8}

Explanation:

Use the facts that d/dx(c * f(x))=c * f'(x) for any constant c, d/dx(arcsin(x))=1/sqrt{1-x^2} and the Chain Rule d/dx(f(g(x)))=f'(g(x)) * g'(x):

f'(x)=3*1/sqrt{1-(x^4)^2} * 4x^3=(12x^3)/sqrt{1-x^8}

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