Risolvere: $\frac{d}{dx}\left(\log \left(\frac{\left(2y+1\right)^5}{\sqrt{y^2+1}}\right)\right)$
Esercizio
$\frac{dy}{dx}\log\left(\frac{\left(2y+1\right)^5}{\sqrt{y^2+1}}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(log(((2*y+1)^5)/((y^2+1)^(1/2)))). Applicare la formula: \frac{d}{dx}\left(x\right)=y=x, dove d/dx=\frac{d}{dx}, d/dx?x=\frac{d}{dx}\left(\log \left(\frac{\left(2y+1\right)^5}{\sqrt{y^2+1}}\right)\right) e x=\log \left(\frac{\left(2y+1\right)^5}{\sqrt{y^2+1}}\right). Applicare la formula: y=x\to \ln\left(y\right)=\ln\left(x\right), dove x=\log \left(\frac{\left(2y+1\right)^5}{\sqrt{y^2+1}}\right). Applicare la formula: y=x\to y=x, dove x=\ln\left(\log \left(\frac{\left(2y+1\right)^5}{\sqrt{y^2+1}}\right)\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(\log \left(\frac{\left(2y+1\right)^5}{\sqrt{y^2+1}}\right)\right).
d/dx(log(((2*y+1)^5)/((y^2+1)^(1/2))))
Risposta finale al problema
$\frac{y^{\prime}}{y}=\frac{1}{\ln\left(10\right)\log \left(\frac{\left(2y+1\right)^5}{\sqrt{y^2+1}}\right)}\left(\frac{10}{2y+1}y^{\prime}+2\left(\frac{-1}{2\left(y^2+1\right)}\right)y\cdot y^{\prime}\right)$