Reviewed by Camille Ira B. Mendoza
What is the derivative of sec x?
Answer: The derivative of sec x is sec x tan x
The derivative of sec x is a fundamental result in calculus, often encountered when differentiating trigonometric functions. Knowing this derivative is essential for solving a variety of problems in mathematics, physics, and engineering that involve rates of change of trigonometric functions.
Methods
Math Tutor Explanation Using the Quotient Rule
Since sec x can be rewritten as 1/cos x, you can use the quotient rule to find its derivative.
Step 1: Step 1: Let f(x) = 1 and g(x) = cos x so that sec x = f(x)/g(x)
Step 2: Step 2: Apply the quotient rule: (f/g)' = (f'g - fg')/g^2
Math Tutor Explanation Using the Chain Rule
By expressing sec x as (cos x)^{-1}, the chain rule can be applied to find its derivative.
Step 1: Step 1: Rewrite sec x as (cos x)^{-1}
Step 2: Step 2: Differentiate using the chain rule, resulting in -1 * (cos x)^{-2} * (-sin x)
Step 1:
Step 2:
Math Tutor suggests: Dive Deeper into Derivatives and Calculus
Expand your calculus skills with these related questions on derivatives and integrals.
FAQ on Derivatives of Trigonometric Functions
What is the derivative of sec x in terms of sine and cosine?
It is (sin x)/(cos^2 x).
Is the derivative of sec x the same as the derivative of 1/cos x?
Yes, since sec x = 1/cos x, their derivatives are the same.
Can the derivative of sec x be negative?
The value of sec x tan x can be negative depending on the interval for x.
How do you remember the derivative of sec x?
A common mnemonic is 'secant's derivative is itself times tangent.'
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