Find derivative: (write answer as single fraction)
y=ln((4x-1)/x^3)
So far I have:
y'=(4/(4x-1))-3/x
How do I write as single fraction
duplicate.
To simplify the expression and write it as a single fraction, we need to find a common denominator.
First, let's simplify the denominators:
Denominator 1: 4x - 1
Denominator 2: x
The common denominator will be (4x - 1) * x.
Now, let's convert both fractions to have the same denominator:
Fraction 1: 4/(4x - 1)
Multiply the numerator and denominator by x to get:
4x/(x(4x - 1))
Fraction 2: -3/x
Multiply the numerator and denominator by (4x - 1) to get:
-3(4x - 1)/(x(4x - 1))
Now, combining both fractions, we get:
(4x - 12x + 3)/(x(4x - 1))
Simplifying further, we get:
(-8x + 3)/(x(4x - 1))
Therefore, the derivative of y = ln((4x - 1)/x^3) can be written as:
y' = (-8x + 3)/(x(4x - 1))