What Is the Derivative of Inverse Tangent?


Quick Answer

The derivative of an inverse tangent is denoted by the formula: y = tan^-1 x. Given that the function has a restricted domain of pi, its derivative is: d / dx (tan^-1 x) = 1 / (1 + x^2). This is the basic derivative of an inverse tangent, meaning that the value of x can be substituted for any angle within its domain to get an actual figure.

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Full Answer

The first step in finding the derivative of an inverse tangent is to graph its function to determine its limits as it approaches infinity. Since the tangent and the inverse tangent functions are inverse functions of one another, they are expressed as: f(x) = tan x and g(x) = tan^-1 x.

By finding the derivative of g(x), the intermediate function incorporates f(x) to result in a singular fraction that has the secant and the inverse tangent as its denominator. The denominator is then simplified to a term that has the tangent as the only unknown, which is further simplified to obtain the finished derivative of the inverse tangent function.

There are five other trigonometric functions: sine, cosine, tangent, cosecant and secant. They all have derivatives that can be determined using the above method.

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