The inverse tangent — known as arctangent or shorthand as arctan, is usually notated as tan-1(some function). To lớn differentiate it quickly, we have two options:1.) Use the simple derivative rule.

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2.) Derive the derivative rule, và then apply the rule.In this lesson, we show the derivative rule for tan-1(u) và tan-1(x). There are four example problems lớn help your understanding.At the kết thúc of the lesson, we will see how the derivative rule is derived.


The derivative rule for arctan(u) is given as:

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The function f(x) = arctan(x) graphed for a single period.

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Since arctangent means inverse tangent, we know that arctangent is the inverse function of tangent. Therefore, we may prove the derivative of arctan(x) by relating it as an inverse function of tangent. Here are the steps for deriving the arctan(x) derivative rule.1.) y = arctan(x), so x = tan(y)2.) dx/dy = sec2(y)3.) Using sum of squares corollary: sec2(y) = 1 + tan2(y)4.) tan2(y) = x2 so dx/dy = 1 + x25.) Flipping dx/dy, we get dy/dx = 1/(1 + x2)