Esercizio
$\frac{d}{dx}\log x^2\sqrt{3x^2-1}$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(log(x)^2(3x^2-1)^(1/2)). Applicare la formula: \frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right), dove d/dx=\frac{d}{dx}, ab=\log \left(x\right)^2\sqrt{3x^2-1}, a=\log \left(x\right)^2, b=\sqrt{3x^2-1} e d/dx?ab=\frac{d}{dx}\left(\log \left(x\right)^2\sqrt{3x^2-1}\right). Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), dove a=2 e x=\log \left(x\right). Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), dove a=\frac{1}{2} e x=3x^2-1. Applicare la formula: x^1=x.
d/dx(log(x)^2(3x^2-1)^(1/2))
Risposta finale al problema
$\frac{2\sqrt{3x^2-1}\log \left(x\right)}{\ln\left(10\right)x}+\frac{3\log \left(x\right)^2x}{\sqrt{3x^2-1}}$