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The derivative of arctan x is 1 (1 x^2). We can prove this either by using the first principle or by using the chain rule. Learn more about the derivative of arctan x along with its proof and solved examples.

This page breaks down the derivatives of inverse trigonometric functions such as arcsin, arccos, arctan, arccot, arccsc, and arcsec. You’ll find a formula reference sheet, and many practice problems with answers to help you master this essential calculus skill.

Derivative of arc tangent function or arctan (x) is 1 (1 x2). The arctan x represents the angle whose tangent is x. In other words, if y = arctan (x), then tan (y) = x. The derivative of a function can be found using the chain rule.

In this lesson, we go over how to find the derivative of arctan through two different methods. We then go over some example problems with solutions.

Proof 2 ... Also presented as The derivative of the arctangent function can also be presented in the form: d(arctan x) dx = 1 x2 1 d (arctan x) d x = 1 x 2 1 Also see Derivative of Arcsine Function Derivative of Arccosine Function Derivative of Arccotangent Function Derivative of Arcsecant Function Derivative of Arccosecant Function Sources

Unfortunately, we want the derivative as a function of x, not of y. We must now plug in the original formula for y, which was y = tan−1 x, to get y = cos2(arctan(x)). This is a correct answer but it can be simplified tremendously. We’ll use some geometry to simplify it.

Derivative of arctan explained clearly—why does it look like that? Follow the formula idea, proof logic, and real examples step by step.

Learn the intricacies of differentiating arctan (x) with clear explanations, derivation steps, examples, and tips to avoid mistakes.

The inverse tangent function, arctan (x), is foundational in calculus, trigonometry, and many applied sciences. Its derivative, [arctan (x)]’ = 1 (1 x²), often appears in integration problems, differential equations, and modeling phenomena in physics and engineering.

Derivative of arctan What is the derivative of the arctangent function of x? The derivative of the arctangent function of x is equal to 1 divided by (1 x 2)

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