differentiate f(x) = [ ln x ]^ 3 i applied the chain rule to obtain 3lnx^2...... do i have to do something else because of absolute value?

Question

anonymous · Answer

chain rule in this case would be aslo require the derivative of what's in the brackets:
$$f(x) = (lnx)^3$$
$$f'(x) = 3(lnx)^2*(\frac{1}{x})$$

anonymous · Answer

ahh i see, the ln is one over x.....thank you !

anonymous · Answer

yeah, so you bring the exponent out front, keep what's in the brackets, reduce the exponent, and then multiply by the derivative of what's in the brackets

anonymous · Answer

would there ever be a scenario like [lnx^2]^3  and would the derivative be 6(lnx)^2*(1/x^2)

anonymous · Answer

ohcorrection *(1/2x)

anonymous · Answer

yes, that is the chain rule with in a chain rule

anonymous · Answer

but the derivative of lnx is still be 1/x...i have to go but can dscribe it better tomorrow if your around

anonymous · Answer

yes i probably will be..... thank you for your help