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TEA [102]
3 years ago
12

Solve this URGENT! Differentiation

Mathematics
1 answer:
Sophie [7]3 years ago
6 0

Instead of using the quotient rule, you can first expand <em>y</em> :

<em>y</em> = (4<em>x</em> - 1)^2 / <em>x</em> ^2 = (16<em>x</em> ^2 - 8<em>x</em> + 1) / <em>x</em> ^2 = 16 - 8/<em>x</em> + 1/<em>x</em> ^2

Then the derivative is

d<em>y</em>/d<em>x</em> = -8/<em>x</em> ^2 - 2/<em>x</em> ^3

The tangent to the curve at (-1, 25) then has a slope or gradient of

d<em>y</em>/d<em>x</em> = -8/(-1)^2 - 2/(-1)^3 = -6

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