Derivative of Sec x: Using Quotient Rule and Cos x Derivative.

Derivative of sec x

To find the derivative of sec x, we will use the quotient rule and the derivative of cos x

To find the derivative of sec x, we will use the quotient rule and the derivative of cos x.

Recall that the secant function can be expressed as sec x = 1 / cos x.

Using the quotient rule, the derivative of sec x can be expressed as:

sec'(x) = (cos(x) * 0 – 1 * sin(x)) / (cos(x))^2

Simplifying this expression, we have:

sec'(x) = -sin(x) / (cos(x))^2

To further simplify, we can use the trigonometric identity sin^2(x) + cos^2(x) = 1 to rewrite the denominator:

sec'(x) = -sin(x) / (cos(x))^2 = -sin(x) / (1 – sin^2(x)) = -sin(x) / cos^2(x)

Therefore, the derivative of sec x is -sin(x) / cos^2(x).

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