How do you find the derivatives of y=(3x-2)/(4x+3) by logarithmic differentiation?

1 Answer
Mar 30, 2017

see below

Explanation:

Use the Property color(red)(log_b(x/y)=log_bx-log_by

Steps in Logarithmic Differentiation:

1. Take natural logarithms of both sides of an equation y=f(x)   and use the Laws of Logarithms to simplify.
2. Differentiate implicitly with respect to x
3. Solve the resulting equation for y’
   4. Replace y with the original equation

color(blue)(ln y = ln ((3x-2)/(4x+3))

color(blue)(ln y = ln (3x-2)-ln(4x+3))

color(blue)(d/dx[ln y = ln (3x-2)-ln(4x+3)]

color(blue)(1/y dy/dx = 3/(3x-2)-4/(4x+3)

color(blue)(dy/dx = [3/(3x-2)-4/(4x+3)]*y

color(blue)(dy/dx = [3/(3x-2)-4/(4x+3)]*[(3x-2)/(4x+3)]