Esercizio
$\frac{d}{dx}\left(x^x\right)\left(5x-2\right)^4\cdot\left(3x^2+5\right)^4$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(x^x(5x-2)^4(3x^2+5)^4). 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(5x-2\right)^4\left(3x^2+5\right)^4, a=x^x, b=\left(5x-2\right)^4\left(3x^2+5\right)^4 e d/dx?ab=\frac{d}{dx}\left(x^x\left(5x-2\right)^4\left(3x^2+5\right)^4\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(5x-2\right)^4\left(3x^2+5\right)^4, a=\left(5x-2\right)^4, b=\left(3x^2+5\right)^4 e d/dx?ab=\frac{d}{dx}\left(\left(5x-2\right)^4\left(3x^2+5\right)^4\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=5x-2. 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=3x^2+5.
d/dx(x^x(5x-2)^4(3x^2+5)^4)
Risposta finale al problema
$\left(\ln\left(x\right)+1\right)x^x\left(5x-2\right)^4\left(3x^2+5\right)^4+x^x\left(20\left(5x-2\right)^{3}\left(3x^2+5\right)^4+24\left(5x-2\right)^4\left(3x^2+5\right)^{3}x\right)$