Change the root to an fractional exponential
Take natural logs of both sides:
Use the property of logarithms that allows us to
move the exponent (1/3) in front of the ln.
Clear the fraction by multiplying both sides by 3
On the right side, write the log of a quotient as
the log of the numerator minus the log of the
denominator.
On the right side, use the fact that the log of
a product is the sum of the logs:
On the right side write the 4 exponent in front of the log.
Remove the largest parentheses:
Take the derivative of both sides, using:
The derivative of a natural log of an expression
is the derivative of the expression divided by
the expression:
Put the 4 in the numerator in the first term on the right:
Divide both sides by 3:
Multiply both sides by f(x)
Substitute for f(x) from the original equation
Edwin
