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## Homework Statement

Find the derivative of:

[itex]\frac{(x^{3} + 5x^{2} − 9x + 4)^{3/4}}{(x^{4} − x^{3} + x^{2} − x + 1)([x^{5} − x^{-5}]^{1/2})}[/itex]

## Homework Equations

Product Rule

Quotient Rule

## The Attempt at a Solution

I've attempted using the quotient rule for the entire thing and gotten a big mess. Is there an easier way which may include breaking it down first?

So basically I wanted to use the quotient rule, meaning I need the derivative of the numerator and denominator and I got...

Numerator:

[itex]\frac{3/4{(3x^{2} + 10x - 9)(x^{3} + 5x^{2} - 9x + 4)^{-1/4}}}{}[/itex]

Denominator:

[itex]\frac{1/2(5x^{4} + 5x^{-6})(x^{5} - x^{-5})^{-1/2}(x^{4}-x^{3}+x^{2}-x+1) + ([x^{5} − x^{-5}]^{1/2})(4x^{3} - 3x^{2} + 2x - 1)}{}[/itex]

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