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Note: I love your Instructions from the Expert, very humorous!

Thank you for taking my question, it is:

If f(x)=(3x^(2)-5)/2x find f'(x)

Since we have f(x) = g(x)/h(x), we know that f'(x) [h(x)g'(x) - g(x)h'(x)]/h(x).
Since g(x) = 3x-5 and h(x) = 2x, it can be seen that g'(x) = 6x and h'(x) = 2.

Putting these in gives f'(x) = [2x*6x - (3x-5)2]/(4x).
That works out to be f'(x) = (12x - 6x - 10)/(4x).

Combining terms gives f'(x) = (6x - 10)/(4x).

Dividing top and bottom by 2 gives f'(x) = (3x - 5)/(2x).

That look right to you?


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