Exercise
$\frac{d}{dx}\left(\ln\left(\frac{2x-3}{x^2-3x+1}\right)\right)$
Step-by-step Solution
Learn how to solve limits by direct substitution problems step by step online. Find the derivative of ln((2x-3)/(x^2-3x+1)). Simplify the derivative by applying the properties of logarithms. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}.
Find the derivative of ln((2x-3)/(x^2-3x+1))
Final answer to the exercise
$\frac{2}{2x-3}+\frac{-2x+3}{x^2-3x+1}$