Esercizio
$\frac{d}{dx}\left(\frac{x\sqrt{x-7}}{\left(3x-8\right)^4}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. Find the derivative d/dx((x(x-7)^(1/2))/((3x-8)^4)). 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\sqrt{x-7}}{\left(3x-8\right)^4}\right) e x=\frac{x\sqrt{x-7}}{\left(3x-8\right)^4}. Applicare la formula: y=x\to \ln\left(y\right)=\ln\left(x\right), dove x=\frac{x\sqrt{x-7}}{\left(3x-8\right)^4}. Applicare la formula: y=x\to y=x, dove x=\ln\left(\frac{x\sqrt{x-7}}{\left(3x-8\right)^4}\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=\ln\left(x\right)+\frac{1}{2}\ln\left(x-7\right)-4\ln\left(3x-8\right).
Find the derivative d/dx((x(x-7)^(1/2))/((3x-8)^4))
Risposta finale al problema
$\left(\frac{1}{x}+\frac{1}{2\left(x-7\right)}+\frac{-12}{3x-8}\right)\frac{x\sqrt{x-7}}{\left(3x-8\right)^4}$