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-Dominant- [34]
3 years ago
8

Explain why the quotient rule is used to determine the derivative of tan x and cot x

Advanced Placement (AP)
1 answer:
otez555 [7]3 years ago
6 0

The quotient rule is used to find the derivative of a ratio between two functions.  It is used in the case of tan(x) and cot(x) because tan(x) can be written as \frac{sin(x)}{cos(x)} (so f(x) = tan(x) is really f(x) = \frac{sin(x)}{cos(x)}).  Similarly, cot(x) can be written as \frac{cos(x)}{sin(x)}, so the quotient rule also applies.

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Answer/Explanation:

We would solve for the value of x in each case.

1. 4x = 12

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26 - 14 = x (subtraction property of equality)

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\frac{56}{8} = x (division property of equality)

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x = -18 (multiplication property of equality)

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x = 16 - 6 (subtraction property of equality)

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18. 10x = 70

x = \frac{70}{10} (division property of equality)

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19. -11 = \frac{x}{3}

-11 \times 3 = x (multiplication property of equality)

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x = 1 + 5 (addition property of equality)

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