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Find the derivative of ln((x^2+1)/(x+3))^0.5

\frac{d}{dx}\left(\sqrt{\ln\left(\frac{x^2+1}{x+3}\right)}\right)

Step by step solution

Problem

$\frac{d}{dx}\left(\sqrt{\ln\left(\frac{x^2+1}{x+3}\right)}\right)$

Show full step-by-step solution

Answer

$\frac{1}{2}\ln\left(\frac{1+x^2}{3+x}\right)^{-\frac{1}{2}}\cdot\frac{3+x}{1+x^2}\cdot\frac{d}{dx}\left(\frac{1+x^2}{3+x}\right)$

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$\frac{d}{dx}\left(\sqrt{\ln\left(\frac{x^2+1}{x+3}\right)}\right)$

Main topic:

Differential calculus

Used formulas:

1. See formulas

Time to solve it:

0.29 seconds