Esercizio
$\frac{d}{dx}\left(3x^4y^5+\frac{\left(5y^3\right)}{\left(6x^2\right)}=\:7xy\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(3x^4y^5+(5y^3)/(6x^2)=7xy). Applicare la formula: \frac{d}{dx}\left(a=b\right)=\frac{d}{dx}\left(a\right)=\frac{d}{dx}\left(b\right), dove a=3x^4y^5+\frac{5y^3}{6x^2} e b=7xy. Applicare la formula: \frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\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=xy, a=x, b=y e d/dx?ab=\frac{d}{dx}\left(xy\right). Applicare la formula: \frac{d}{dx}\left(x\right)=1.
d/dx(3x^4y^5+(5y^3)/(6x^2)=7xy)
Risposta finale al problema
$3\left(4x^{3}y^5+5x^4y^{4}y^{\prime}\right)+\frac{90y^{2}y^{\prime}x^2-60y^3x}{36x^{4}}=7\left(y+xy^{\prime}\right)$