Esercizio
$\frac{d}{dx}\left(\left(x+1\right)^2\left(x^2+1\right)^{-3}=y\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx((x+1)^2(x^2+1)^(-3)=y). Applicare la formula: \frac{d}{dx}\left(a=b\right)=\frac{d}{dx}\left(a\right)=\frac{d}{dx}\left(b\right), dove a=\left(x+1\right)^2\left(x^2+1\right)^{-3} e b=y. Applicare la formula: \frac{d}{dx}\left(x\right)=1. 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=\left(x+1\right)^2\left(x^2+1\right)^{-3}, a=\left(x+1\right)^2, b=\left(x^2+1\right)^{-3} e d/dx?ab=\frac{d}{dx}\left(\left(x+1\right)^2\left(x^2+1\right)^{-3}\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=x+1.
d/dx((x+1)^2(x^2+1)^(-3)=y)
Risposta finale al problema
$\frac{2\left(x+1\right)}{\left(x^2+1\right)^{3}}+\frac{-6\left(x+1\right)^2x}{\left(x^2+1\right)^{4}}=y^{\prime}$