Esercizio
$\frac{d}{dx}cosh^{-1}secy=xy^3$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(cosh(y)^(-1)sec(y)=xy^3). Applicare la formula: \frac{d}{dx}\left(a=b\right)=\frac{d}{dx}\left(a\right)=\frac{d}{dx}\left(b\right), dove a=\mathrm{cosh}\left(y\right)^{-1}\sec\left(y\right) e b=xy^3. Applicare la formula: \frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right), dove d/dx=\frac{d}{dx}, ab=\mathrm{cosh}\left(y\right)^{-1}\sec\left(y\right), a=\mathrm{cosh}\left(y\right)^{-1}, b=\sec\left(y\right) e d/dx?ab=\frac{d}{dx}\left(\mathrm{cosh}\left(y\right)^{-1}\sec\left(y\right)\right). Applicare la formula: \frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right), dove d/dx=\frac{d}{dx}, ab=xy^3, a=x, b=y^3 e d/dx?ab=\frac{d}{dx}\left(xy^3\right). Applicare la formula: \frac{d}{dx}\left(x\right)=1.
d/dx(cosh(y)^(-1)sec(y)=xy^3)
Risposta finale al problema
$\frac{-1}{\mathrm{cosh}\left(y\right)^{2}}y^{\prime}\mathrm{sinh}\left(y\right)\sec\left(y\right)+\frac{1}{\mathrm{cosh}\left(y\right)}y^{\prime}\sec\left(y\right)\tan\left(y\right)=y^3+3xy^{2}y^{\prime}$