Sunday
April 20, 2014

Homework Help: Derivatives

Posted by Erika on Friday, May 24, 2013 at 1:35am.

Find f'(x): (abs(((x^2)*((3x+2) ^(1/3)))/((2x-3)^3))

So I thought I should split it into two parts: A and B.

A) (x^2)/((2x-3)^2)
B) ((3x+2)^(1/3))/(2x-3)

My plan was to differentiate each part and then multiply them together, since multiplying their denominators together gives me the original denominator power (4).

I end up getting for A) (-12x^2 + 18x)/((2x-3)^4)

For B, I have something which seems much more complex, because of the negative fractional exponents, and this is where I'm stuck. I want to simplify, but I'm not sure how to without screwing everything up. This is my last step for B:

((3x+2)^(-2/3)*(2x-3) - 4(x-3)*((3x+2)^(1/3)))/((2x-3)^2)

I really appreciate the help. And also, as for the absolute value part of the question, well I haven't even thought about that- I'm stuck on the easy part itself. -_-

Thank you!

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