121616949-math.69

# 121616949-math.69 - x 2 is a particularly simple...

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3.4 The Quotient Rule 55 With a bit of algebra, both of these simplify to - x 2 + 625 2 625 - x 2 x 3 / 2 . Occasionally you will need to compute the derivative of a quotient with a constant numerator, like 10 /x 2 . Of course you can use the quotient rule, but it is usually not the easiest method. If we do use it here, we get d dx 10 x 2 = x 2 · 0 - 10 · 2 x x 4 = - 20 x 3 , since the derivative of 10 is 0. But it is simpler to do this: d dx 10 x 2 = d dx 10 x - 2 = - 20
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Unformatted text preview: x 2 is a particularly simple denominator, but we will see that a similar calcu-lation is usually possible. Another approach is to remember that d dx 1 g ( x ) =-g ± ( x ) g ( x ) 2 , but this requires extra memorization. Using this formula, d dx 10 x 2 = 10-2 x x 4 . Note that we ﬁrst use linearity of the derivative to pull the 10 out in front....
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