Esercizio
$\frac{d}{dx}\left(x^x\right)\left(x+4\right)^4\left(7x-2\right)^3$
Soluzione passo-passo
Impara online a risolvere i problemi di limiti di funzioni esponenziali passo dopo passo. d/dx(x^x(x+4)^4(7x-2)^3). 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^x\left(x+4\right)^4\left(7x-2\right)^3, a=x^x, b=\left(x+4\right)^4\left(7x-2\right)^3 e d/dx?ab=\frac{d}{dx}\left(x^x\left(x+4\right)^4\left(7x-2\right)^3\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\right)^4\left(7x-2\right)^3, a=\left(x+4\right)^4, b=\left(7x-2\right)^3 e d/dx?ab=\frac{d}{dx}\left(\left(x+4\right)^4\left(7x-2\right)^3\right). Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), dove a=4 e x=x+4. Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), dove a=3 e x=7x-2.
Risposta finale al problema
$\left(\ln\left(x\right)+1\right)x^x\left(x+4\right)^4\left(7x-2\right)^3+x^x\left(4\left(x+4\right)^{3}\left(7x-2\right)^3+21\left(x+4\right)^4\left(7x-2\right)^{2}\right)$