Mastering The Derivative Of Sec(X): How To Use Quotient And Chain Rule To Simplify Your Calculus Journey

Derivative of sec(x)

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The derivative of sec(x) can be found using the quotient rule and the chain rule.

sec(x) = 1/cos(x)

Thus, we have:

d/dx [sec(x)] = d/dx [1/cos(x)]

Using the quotient rule, we get:

= [(-1/cos^2(x)) * (-sin(x))] / cos(x)^2

= sin(x) / cos^2(x)

Using the identity, tan(x) = sin(x) / cos(x), we can rewrite this as:

d/dx [sec(x)] = tan(x) * sec(x)

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