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Question

Find f'(x) if f(x)= x^2arccos(lnx^(1/2))

Answer 1

f(x) = x^2 arccos( [ln(x)]^(1/2) )

To solve this, we use the product rule, as well as the chain rule when taking the derivative.

f'(x) = 2x arccos( [ln(x)]^(1/2) ) + x^2 ( 1 / sqrt(1 - [ln(x)]) )
(1/2) [ln(x)]^(-1/2) (1/x)