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Inverse Trigonometric Functions Differentiation Calculator

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Example
Created on 2024-06-20Asked by Aiden Martin (Solvelet student)
Differentiate y=arctan⁡(x) y = \arctan(x) with respect to x x .

Solution

To differentiate y=arctan⁡(x) y = \arctan(x) with respect to x x : We use the known derivative formula for arctan⁡(x) \arctan(x) : ddxarctan⁡(x)=11+x2 \frac{d}{dx} \arctan(x) = \frac{1}{1 + x^2} Therefore, the derivative of y=arctan⁡(x) y = \arctan(x) is: dydx=11+x2 \frac{dy}{dx} = \frac{1}{1 + x^2} Solved on Solvelet with Basic AI Model
Some of the related questions asked by Michael Miller on Solvelet
1. Find the derivative of y=arcsin⁡(2x)y = \arcsin(2x) with respect to xx,2. Show that the mapping ϕ:Z→Z\phi : \mathbb{Z} \rightarrow \mathbb{Z} defined by ϕ(n)=n+5\phi(n) = n + 5 is a homomorphism.,
DefinitionThe process of obtaining derivative of trigonometric function are always related to the inverse trig functions like sin inverse,cos inverse, tan inverse etc. They are tools we use in a lot of calculus problems, integration, differential equations. For Example, The derivative of inverse sine function is ddxsin−1(x)=1Hence,x2−2​Solution, Likewise, the derivative of the inverse tangent function is dxd​tan−1(x)=1+x21​.
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