If the numbers -2.5, -1.6, -3 1/10, - 1/10, and -0.5 were graphed on a number line, which would appear farthest to the left?

1 answer:

7 0

Turn the question around.
If all the numbers were positive: 2.5, 1.6, 3 1/10, 1/10, and 0.5, which would be farthest to the right?

The fact is that the negative numbers are a reflection of the positive numbers.
Since 3 1/10 would be farthest to the right with positive numbers, -3 1/10 will be farthest to the left with the negative numbers.

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Now, let's work it out:
$\frac{dy}{dx} = \frac{1}{sinh(2x) } * \frac{d}{dx}[sinh(2x)]$

Next step:
$\frac{dy}{dx} = \frac{1}{sinh(2x) } * cosh(2x) * \frac{d}{dx}[2x]$

Next step:
$\frac{dy}{dx} = \frac{1}{sinh(2x) } * cosh(2x) *2$

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$\frac{dy}{dx} = \frac{2cosh(2x)}{sinh(2x) }$

Simplify further:
$\frac{dy}{dx} = 2 (\frac{cosh(2x)}{sinh(2x)})$

Remember that:
${\frac{cosh(x)}{sinh(x)} = coth(x)$

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$\boxed{ \frac{dy}{dx} = 2coth(2x) }$

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