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$\begingroup$

$$K = \frac{-(\sigma^2 + 3\sigma + 2)}{\sigma^2 - 8\sigma +15}$$

How is this differentiated with respect to $\sigma$?

The answer is

$$\dfrac{dK}{d\sigma} = \frac{11\sigma^2 - 26\sigma -61}{(\sigma^2 - 8\sigma + 15)^2}$$

And the quotient rule is a very long process, I get the feeling there was a short method.

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    It's just the quotient rule. $(f/g)'={f'g-g'f\over g^2}$. Your comment about partial fractions leads me to say "the derivative, not the indefinite integral"...2011-11-08
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    That would be the quotient rule... partial fractions is an integration technique, not differentiation.2011-11-08
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    Er I meant quotient, I was tired2011-11-08
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    Oh thanks, I didn't know that rule2011-11-08

2 Answers 2