Risolvere: $\frac{d}{dx}\left(\frac{\left(x^2+12\right)^5\left(x^3+17\right)^4}{x-3}\right)$
Esercizio
$\frac{dy}{dx}\left(\frac{\left(\left(x^2+12\right)^5\left(x^3+17\right)^4\right)}{x-3}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. Find the derivative d/dx(((x^2+12)^5(x^3+17)^4)/(x-3)). 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{\left(x^2+12\right)^5\left(x^3+17\right)^4}{x-3}\right) e x=\frac{\left(x^2+12\right)^5\left(x^3+17\right)^4}{x-3}. Applicare la formula: y=x\to \ln\left(y\right)=\ln\left(x\right), dove x=\frac{\left(x^2+12\right)^5\left(x^3+17\right)^4}{x-3}. Applicare la formula: y=x\to y=x, dove x=\ln\left(\frac{\left(x^2+12\right)^5\left(x^3+17\right)^4}{x-3}\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=5\ln\left(x^2+12\right)+4\ln\left(x^3+17\right)-\ln\left(x-3\right).
Find the derivative d/dx(((x^2+12)^5(x^3+17)^4)/(x-3))
Risposta finale al problema
$\left(\frac{10x}{x^2+12}+\frac{12x^{2}}{x^3+17}+\frac{-1}{x-3}\right)\frac{\left(x^2+12\right)^5\left(x^3+17\right)^4}{x-3}$