Esercizio
$\frac{d}{dx}\left(y=X^2\sqrt{7-2x}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(y=x^2(7-2x)^(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=y e b=x^2\sqrt{7-2x}. 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=x^2\sqrt{7-2x}, a=x^2, b=\sqrt{7-2x} e d/dx?ab=\frac{d}{dx}\left(x^2\sqrt{7-2x}\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=7-2x.
Risposta finale al problema
$y^{\prime}=2x\sqrt{7-2x}+\frac{-x^2}{\sqrt{7-2x}}$