What is the derivative of #ln[(x(x^2+1)^2)/(2x^3-1)^(1/2)] #?
1 Answer
Apr 7, 2017
Use laws of logarithms, letting the function be
#f(x) = lnx + ln(x^2 + 1)^2 - ln(2x^3 - 1)^(1/2)#
#f(x) = lnx + 2ln(x^2 + 1) - 1/2ln(2x^3 - 1)#
Now use the chain rule on each term.
#f'(x) = 1/x + (4x)/(x^2 + 1) - (6x^2)/(2(2x^3 - 1))#
#f'(x) = 1/x + (4x)/(x^2 + 1) - (3x^2)/(2x^3 - 1)#
Hopefully this helps!
