Răspuns:
Salutare!
Explicație pas cu pas:
1.
[tex] \frac{d}{dx} (x {}^{2} y) = \frac{d}{dx} (891)[/tex]
2
[tex] \frac{d}{dx} ( {x}^{2} ) \times y + {x}^{2} \times \frac{d}{dx} (y) = \frac{d}{dx} (891[/tex]
3.
[tex] \frac{d}{dx} (x {}^{2} ) \times y + x {}^{2} \times \frac{x}{dx} (y) = 0[/tex]
4.
[tex]2xy + {x}^{2} \times \frac{d}{dx} (y) = 0[/tex]
5.
[tex]2xy + {x}^{2} \times \frac{d}{dy} (y) \times \frac{dy}{dx} = 0[/tex]
6.
[tex]2xy \times {x}^{2} \times 1 \times \frac{dy}{dx} = 0[/tex]
7.
[tex]2xy + {x}^{2} \times \frac{dy}{dx} = 0[/tex]
8.
[tex]2xy + {x}^{2} \times \frac{dy}{dx} - 2xy = 0 - 2xy[/tex]
9.
[tex] {x}^{2} \times \frac{dy}{dx} = 0 - 2xy [/tex]
10.
[tex] {x}^{2} \times \frac{dx}{xy} = -2 xy[/tex]
11.
[tex] {x}^{2} \times \frac{dy}{dx} + \div 2 = 2xy \div {x}^{2} [/tex]
12.
[tex] \frac{dy}{dx} = - 2x \div {x}^{2} [/tex]
13.
[tex] \frac{dy}{dx} = - \frac{2xy}{ {x}^{2} } [/tex]
14.
[tex] \frac{dy}{dx} = \frac{2y}{x} [/tex]
