Q. 86 Use the quotient rule and the de... [FREE SOLUTION]

Chapter 2: Q. 86 (page 235)

Use the quotient rule and the derivatives of the sine and cosine functions to prove that $\frac{d}{d x} (c o t x) = - c s c^{2} x$ .

Short Answer

Expert verified

We proved $\frac{d}{d x} (c o t x) = - c s c^{2} x$ .

Step by step solution

Step 1. Given Information

We are given $c o t x$ and using the quotient rule and the derivatives of the sine and cosine functions we need to prove that $\frac{d}{d x} (c o t x) = - c s c^{2} x$ .

Step 2. Proving the expression

$\frac{d}{d x} (c o t x) = \frac{d}{d x} (\frac{\cos x}{\sin x})$

Using the quotient rule we get,

$= \frac{(\frac{d}{d x} (\cos x)) \sin x - \cos x (\frac{d}{d x} (\sin x))}{\sin^{2} x} = \frac{- \sin x \sin x - \cos x \cos x}{\sin^{2} x} = \frac{- (\sin^{2} x + \cos^{2} x)}{\sin^{2} x} = \frac{- 1}{\sin^{2} x} = - c s c^{2} x$

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Use the quotient rule and the derivatives of the sine and cosine functions to prove that $\frac{d}{d x} (c o t x) = - c s c^{2} x$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Proving the expression

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91影视

Use the quotient rule and the derivatives of the sine and cosine functions to prove thatddxcotx=-csc2x.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Proving the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Probability and Statistics

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Use the quotient rule and the derivatives of the sine and cosine functions to prove that $\frac{d}{d x} (c o t x) = - c s c^{2} x$ .