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