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Apply the formula: $\frac{d}{dx}\left(\arctan\left(\theta \right)\right)$$=\frac{1}{1+\theta ^2}\frac{d}{dx}\left(\theta \right)$, where $x=x-\sqrt{1+x^2}$
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$\frac{1}{1+\left(x-\sqrt{1+x^2}\right)^2}\frac{d}{dx}\left(x-\sqrt{1+x^2}\right)$
Learn how to solve problems step by step online. d/dx(arctan(x-(1+x^2)^(1/2))). Apply the formula: \frac{d}{dx}\left(\arctan\left(\theta \right)\right)=\frac{1}{1+\theta ^2}\frac{d}{dx}\left(\theta \right), where x=x-\sqrt{1+x^2}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the formula: \frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right). Apply the formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), where a=\frac{1}{2} and x=1+x^2.
