Esercizio
$\frac{d}{dx}\sqrt{x}e^{x^2}\left(x^2+5\right)^9$
Soluzione passo-passo
Impara online a risolvere i problemi di limiti per sostituzione diretta passo dopo passo. d/dx(x^(1/2)e^x^2(x^2+5)^9). 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=\sqrt{x}e^{\left(x^2\right)}\left(x^2+5\right)^9, a=\sqrt{x}, b=e^{\left(x^2\right)}\left(x^2+5\right)^9 e d/dx?ab=\frac{d}{dx}\left(\sqrt{x}e^{\left(x^2\right)}\left(x^2+5\right)^9\right). 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=e^{\left(x^2\right)}\left(x^2+5\right)^9, a=e^{\left(x^2\right)}, b=\left(x^2+5\right)^9 e d/dx?ab=\frac{d}{dx}\left(e^{\left(x^2\right)}\left(x^2+5\right)^9\right). Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), dove a=9 e x=x^2+5. Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}.
d/dx(x^(1/2)e^x^2(x^2+5)^9)
Risposta finale al problema
$\frac{e^{\left(x^2\right)}\left(x^2+5\right)^9}{2\sqrt{x}}+2\sqrt{x^{3}}e^{\left(x^2\right)}\left(x^2+5\right)^9+18\sqrt{x^{3}}e^{\left(x^2\right)}\left(x^2+5\right)^{8}$