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2. Derivatives of Csc, Sec and Cot Functions

by M. Bourne

By using the quotient rule and trigonometric identities, we can obtain the following derivatives:

In words, we would say:

The derivative of csc x is -csc x cot x,
The derivative of sec x is sec x tan x and
The derivative of cot x is -csc²x.

If u = f(x) is a function of x, then by using the chain rule, we have:

 

Example 1:

Find the derivative of s = sec(3t + 2).

Answer

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Example 2:

Find the derivative of x = θ³ csc 2θ.

Answer

 

Example 3:

Find the derivative of y = sec⁴3x.

Answer

Exercises

1. Find the derivative of y = csc²(2x²).

 

Answer

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2. Find the derivative of y = sec² 2x.

Answer

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3. Find the derivative of 3 cot(x + y) = cos y².

Answer

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Chapter Contents

• Differentiation of Transcendental Functions
• 1. Derivatives of Sin, Cos and Tan Functions
• 2. Derivatives of Csc, Sec and Cot Functions
• 3. Derivatives of Inverse Trigonometric Functions
• 4. Applications: Derivatives of Trigonometric Functions
• 5. Derivative of the Logarithmic Function
• 6. Derivative of the Exponential Function
• 7. Applications: Derivatives of Logarithmic and Exponential Functions

• Comments, Questions?

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