Aprenda online a resolver problemas passo a passo. d/dx(ln(arctan(2x^2))^(1/2)). Aplicamos a regra: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), onde a=\frac{1}{2} e x=\ln\left(\arctan\left(2x^2\right)\right). Aplicamos a regra: \frac{d}{dx}\left(\ln\left(x\right)\right)=\frac{1}{x}\frac{d}{dx}\left(x\right). Aplicamos a regra: \frac{a}{b}\frac{c}{f}=\frac{ac}{bf}, onde a=1, b=2, c=1, a/b=\frac{1}{2}, f=\arctan\left(2x^2\right), c/f=\frac{1}{\arctan\left(2x^2\right)} e a/bc/f=\frac{1}{2}\ln\left(\arctan\left(2x^2\right)\right)^{-\frac{1}{2}}\frac{1}{\arctan\left(2x^2\right)}\frac{d}{dx}\left(\arctan\left(2x^2\right)\right). Aplicamos a regra: \frac{d}{dx}\left(\arctan\left(\theta \right)\right)=\frac{1}{1+\theta ^2}\frac{d}{dx}\left(\theta \right), onde x=2x^2.

d/dx(ln(arctan(2x^2))^(1/2))