use logarithmic differenciation to find the derivative of: g(x) = (3x^5  - 4) (2x^3 +9)                            (7x^4  - 5)   thanks!!      

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Hi Ben - Log differentiation is a GREAT tool when you have a messy rational function to deal with like you were given here.  Let me show you how it works with a simpler example: y = (2x + 3) / (x^2 -4) Step 1: take natural log of both sides ln(y) = ln[ (2x + 3) / (x^2 -4)] Step 2: Dig out the cobwebs and use all the rules of logs that you learned in Algebra II or Pre-Calc. ln(y) = ln(2x + 3) - ln(x^2 -4) Step 3: Take derivative of each ln term with respect to x and don't forget to use "implicit" differentiation on y: (1/y)(dy/dx) = [1/(2x + 3)](2) - [1/(x^2 -4)](2x) Step 4: Multiply both sides of the equation by "y": dy/dx = y{[1/(2x + 3)](2) - [1/(x^2 -4)](2x)} Step 5: Substitute the original value for y on the right side of the equation:  dy/dx = [(2x + 3) / (x^2 -4)]{[1/(2x + 3)](2) - [1/(x^2 -4)](2x)} I know this looks like a big mess, but it sure beats using the product and quotient rule on a messy differentiation problem like you were given. Hope this helps