Question

find the derivative of f(x) = ((x+1)^3/2 (x-4)^5/2)/5x+3^2/3 using logarithmic differentiation

Answer 1

take the log, then simplify using the properties of the log
this is such a mess that i cannot actually read it, but the idea is that
\[\ln(x^r)=r\ln(x)\] and \(\ln(ab)=\ln(a)+\ln(b)\)
when you get done, you should have no exponents and no products of division
then take the derivative term by term. this will now be very easy
then multiply by the original funtion

Answer 2

*products OR divisions, just term that look like
\[\frac{2}{3}\ln(x+2)\] or something

Answer 3

here is a picture to make it more clear, sorry its messy