Esercizio
$\frac{d}{dx}\left(\left(6x+1\right)^{ln\left(5x+7\right)}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di prodotti speciali passo dopo passo. d/dx((6x+1)^ln(5x+7)). Applicare la formula: \frac{d}{dx}\left(a^b\right)=y=a^b, dove d/dx=\frac{d}{dx}, a=6x+1, b=\ln\left(5x+7\right), a^b=\left(6x+1\right)^{\ln\left(5x+7\right)} e d/dx?a^b=\frac{d}{dx}\left(\left(6x+1\right)^{\ln\left(5x+7\right)}\right). Applicare la formula: y=a^b\to \ln\left(y\right)=\ln\left(a^b\right), dove a=6x+1 e b=\ln\left(5x+7\right). Applicare la formula: \ln\left(x^a\right)=a\ln\left(x\right), dove a=\ln\left(5x+7\right) e x=6x+1. Applicare la formula: \ln\left(y\right)=x\to \frac{d}{dx}\left(\ln\left(y\right)\right)=\frac{d}{dx}\left(x\right), dove x=\ln\left(5x+7\right)\ln\left(6x+1\right).
Risposta finale al problema
$\left(\frac{5\ln\left(6x+1\right)}{5x+7}+\frac{6\ln\left(5x+7\right)}{6x+1}\right)\left(6x+1\right)^{\ln\left(5x+7\right)}$