Esercizio
$\frac{d}{dx}\left(\left(x^3+1\right)\left(x^4+2\right)\left(x^5+3\right)^2\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx((x^3+1)(x^4+2)(x^5+3)^2). 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=\left(x^3+1\right)\left(x^4+2\right)\left(x^5+3\right)^2, a=x^3+1, b=\left(x^4+2\right)\left(x^5+3\right)^2 e d/dx?ab=\frac{d}{dx}\left(\left(x^3+1\right)\left(x^4+2\right)\left(x^5+3\right)^2\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=\left(x^4+2\right)\left(x^5+3\right)^2, a=x^4+2, b=\left(x^5+3\right)^2 e d/dx?ab=\frac{d}{dx}\left(\left(x^4+2\right)\left(x^5+3\right)^2\right). Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), dove a=2 e x=x^5+3. Applicare la formula: x^1=x.
d/dx((x^3+1)(x^4+2)(x^5+3)^2)
Risposta finale al problema
$3x^{2}\left(x^4+2\right)\left(x^5+3\right)^2+\left(x^3+1\right)\left(4x^{3}\left(x^5+3\right)^2+10\left(x^4+2\right)\left(x^5+3\right)x^{4}\right)$