How To Find The Derivative Of Sec X Using Quotient Rule Of Differentiation

Derivative of sec x

sec x tan x

The derivative of sec x can be found using the quotient rule of differentiation.

Recall that sec x is defined as 1/cos x. Using the quotient rule, we have:

d(sec x)/dx = (cos x*d(1)/dx – 1*d(cos x)/dx)/(cos x)^2

Simplifying this equation, we can use the fact that d(1)/dx = 0 (since the derivative of a constant is zero) and the chain rule of differentiation, which states that d(cos x)/dx = -sin x.

d(sec x)/dx = (-sin x)/(cos x)^2

Now, we can simplify further by using the trigonometric identity sin^2 x + cos^2 x = 1, which tells us that sin^2 x = 1 – cos^2 x.

Substituting sin^2 x = 1 – cos^2 x and rearranging, we get:

d(sec x)/dx = -sin x/cos x * 1/(cos x) = -tan x*sec x

Therefore, the derivative of sec x is -tan x*sec x.

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