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