Esercizio
$\frac{d}{dx}\left(x^x\right)y=\sqrt{\frac{x-5}{x^8+5}}$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(x^xy=((x-5)/(x^8+5))^(1/2)). Applicare la formula: \frac{d}{dx}\left(a=b\right)=\frac{d}{dx}\left(a\right)=\frac{d}{dx}\left(b\right), dove a=x^xy e b=\sqrt{\frac{x-5}{x^8+5}}. 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=x^xy, a=x^x, b=y e d/dx?ab=\frac{d}{dx}\left(x^xy\right). Applicare la formula: \frac{d}{dx}\left(x\right)=1. 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=\frac{x-5}{x^8+5}.
d/dx(x^xy=((x-5)/(x^8+5))^(1/2))
Risposta finale al problema
$y^{\prime}=\frac{-7x^{8}+5+40x^{7}-2x^xy\sqrt{\left(x^8+5\right)^{3}}\sqrt{x-5}\ln\left(x\right)-2x^xy\sqrt{\left(x^8+5\right)^{3}}\sqrt{x-5}}{2x^x\sqrt{\left(x^8+5\right)^{3}}\sqrt{x-5}}$