Esercizio
$\frac{d}{dx}\left(e^{xy}\left(yseny+xcosy\right)=1\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di calcolo integrale passo dopo passo. d/dx(e^(xy)(ysin(y)+xcos(y))=1). Applicare la formula: \frac{d}{dx}\left(a=b\right)=\frac{d}{dx}\left(a\right)=\frac{d}{dx}\left(b\right), dove a=e^{xy}\left(y\sin\left(y\right)+x\cos\left(y\right)\right) e b=1. Applicare la formula: \frac{d}{dx}\left(c\right)=0, dove c=1. 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=e^{xy}\left(y\sin\left(y\right)+x\cos\left(y\right)\right), a=e^{xy}, b=y\sin\left(y\right)+x\cos\left(y\right) e d/dx?ab=\frac{d}{dx}\left(e^{xy}\left(y\sin\left(y\right)+x\cos\left(y\right)\right)\right). Applicare la formula: \frac{d}{dx}\left(e^x\right)=e^x\frac{d}{dx}\left(x\right), dove x=xy.
d/dx(e^(xy)(ysin(y)+xcos(y))=1)
Risposta finale al problema
$y^{\prime}=\frac{-y^2\sin\left(y\right)-xy\cos\left(y\right)-\cos\left(y\right)}{yx\sin\left(y\right)+x^2\cos\left(y\right)+\sin\left(y\right)+y\cos\left(y\right)-x\sin\left(y\right)}$