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