Calculus/=)

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Expert: - 11/17/2008


Question
y= ((3x^2-1)^5/(x^2+1)^4)
a) find y' by the quotient rule (do not simplify)
b) simply y' completely

Answer
a) Let f(x) = (3x²-1)^5 and g(x) = (x²+1)^4.

It is known that f'(x) = 5(3x²-1)^4(6x), since 6x is the derivative of 3x²-1.

It is also known that g'(x) = 4(x²+1)^3(2x) since 2x is the derivative of x²+1.

The derivative is [g(x)f'(x) - f(x)g'(x)]/g²(x).

b) Does that say simplify completely?  I think what needs to be done is factoring out a [(3x²-1)^4][(x²+1)^3] from the top.  Once this has been done, not that the bottom has (x²+1)^8, so (x²+1)^3 can be cancelled in the top and bottom.  Once this has been done, multiply out what's inside the parenthises and simplify what's on top.  I don't know if they mean to multiply by (3x²-1)^4, though, as this is fairly messy.

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