Let f(x) = an^-1 (( (x2+1))/(sqrt(x2+4))). Find f^(4)(0), the 4th derivative at x=0$.

May 29, 2026Mathematics

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May 29, 2026

Answer

\frac{\ln(x^2+1)}{\sqrt{x^2+4}}$.

Right ThegirlGodishelping🥰💙🫠, let's go.

1. Let $f(x) = \tan^{-1}\left(\frac{\ln(x^2+1)}{\sqrt{x^2+4}}\right)$ . Find $f^{(4)}(0)$ , the 4th derivative at $x=0$ .

Step 1: Analyze the function for symmetry. Let $g(x) = \frac{\ln(x^2+1)}{\sqrt{x^2+4}}$ . $g(-x) = \frac{\ln((-x)^2+1)}{\sqrt{(-x)^2+4}} = \frac{\ln(x^2+1)}{\sqrt{x^2+4}} = g(x)$ . So

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Right ThegirlGodishelping🥰💙🫠, let's go. 1.

Asked on May 29, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 29, 2026

Right ThegirlGodishelping🥰💙🫠, let's go. 1. Let f(x) = ^-1(((x^2+1))/(sqrt(x^2+4))). Find f^(4)(0), the 4th derivative at x=0. Step 1: Analyze the function for symmetry. Let g(x) = ((x^2+1))/(sqrt(x^2+4)). g(-x) = (((-x)^2+1))/(sqrt((-x)^2+4)) = ((x^2+1))/(sqrt(x^2+4)) = g(x). So