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Calculus/Fidn the derivative

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Expert: - 10/18/2008


Question
Find the derivative:   f (x) = ln ((x2√4x + 1) / (x3 + 5)3)

Answer
I will assume the function is f(x) = ln((x²√(4x) + 1) / (x^3 + 5)^3).

The derivative is of the function ln(g(x)).
The derivative is g'(x)/g(x).
g'(x) is found by taking the derivative of h(x)/i(x) where
h(x)=x²√(4x) + 1 and i(x) = (x3 + 5)^3.
h'(x) is a product rule and i(x) is a power rule.

Find all of these and put them back into one complicated messy fraction that can be simplified.  Remember those () for multiplication.

Calculus

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