(\partial)/(\partial y)(x^2yz+1/(xyz^2))

Lösung

\frac{\partial}{\partial y} (x^{2} yz + \frac{1}{x y z ^{2}})

x^{2} z - \frac{1}{x z ^{2} y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{2} yz + \frac{1}{x y z ^{2}})

Behandle

x, z

als Konstanten

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (x^{2} yz) + \frac{\partial}{\partial y} (\frac{1}{x y z ^{2}})

\frac{\partial}{\partial y} (x^{2} yz) = x^{2} z

\frac{\partial}{\partial y} (\frac{1}{x y z ^{2}}) = - \frac{1}{x z ^{2} y ^{2}}

= x^{2} z - \frac{1}{x z ^{2} y ^{2}}

\frac{d y}{d x} = 5 y^{2}, y (0) = 3

t an g e n t f (x) = x^{3} - 15 x, (1, - 14)

t an g e n t \frac{1}{5 x}, at x = 9

t a y l or \frac{1}{( ( 3 - 2 x ) )}

t an g e n t \frac{5 x + 2}{6 x - 4}