Risolvere: $\frac{d}{dx}\left(y=\frac{\left(2x^2+3\right)^2}{\left(x+1\right)^2\left(5x+6\right)}\right)$
Esercizio
$\frac{dy}{dx}\left(y=\frac{\left(2x^2+3\right)^2}{\left(x+1\right)^2\left(5x+6\right)}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(y=((2x^2+3)^2)/((x+1)^2(5x+6))). 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=\frac{\left(2x^2+3\right)^2}{\left(x+1\right)^2\left(5x+6\right)}. Applicare la formula: \frac{d}{dx}\left(x\right)=1. Applicare la formula: \frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}, dove a=\left(2x^2+3\right)^2 e b=\left(x+1\right)^2\left(5x+6\right). Applicare la formula: \left(ab\right)^n=a^nb^n.
d/dx(y=((2x^2+3)^2)/((x+1)^2(5x+6)))
Risposta finale al problema
$y^{\prime}=\frac{4\cdot 2\left(2x^2+3\right)\left(x+1\right)^2x\left(5x+6\right)+\left(2\left(-5x-6\right)\left(x+1\right)-5\left(x+1\right)^2\right)\left(2x^2+3\right)^2}{\left(x+1\right)^{4}\left(5x+6\right)^2}$