Esercizio
$\frac{d}{dx}\left(\frac{x^8\left(x-3\right)^4}{\left(x^2+7\right)^8}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. Find the derivative d/dx((x^8(x-3)^4)/((x^2+7)^8)). Applicare la formula: \frac{d}{dx}\left(x\right)=y=x, dove d/dx=\frac{d}{dx}, d/dx?x=\frac{d}{dx}\left(\frac{x^8\left(x-3\right)^4}{\left(x^2+7\right)^8}\right) e x=\frac{x^8\left(x-3\right)^4}{\left(x^2+7\right)^8}. Applicare la formula: y=x\to \ln\left(y\right)=\ln\left(x\right), dove x=\frac{x^8\left(x-3\right)^4}{\left(x^2+7\right)^8}. Applicare la formula: y=x\to y=x, dove x=\ln\left(\frac{x^8\left(x-3\right)^4}{\left(x^2+7\right)^8}\right) e y=\ln\left(y\right). 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=8\ln\left(x\right)+4\ln\left(x-3\right)-8\ln\left(x^2+7\right).
Find the derivative d/dx((x^8(x-3)^4)/((x^2+7)^8))
Risposta finale al problema
$\left(\frac{8}{x}+\frac{4}{x-3}+\frac{-16x}{x^2+7}\right)\frac{x^8\left(x-3\right)^4}{\left(x^2+7\right)^8}$