(\partial)/(\partial y)(x^2yz^2+sin(yz))

解答

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

x^{2} z^{2} + cos (yz) z

求解步骤

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

将

x, z

视为常数

使用微分加减法定则:

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

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

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

\frac{\partial}{\partial y} (sin (yz)) = cos (yz) z

= x^{2} z^{2} + cos (yz) z

\frac{d x}{d t} = x - x^{2}

\frac{d}{d x} (4^{3 x})

\int \frac{6 x + 4}{x ^{2} ( x ^{2} + 2 )} d x

(x - 2 y) d y + (y + 4 x) d x = 0

d er i v a t i v e 3 x^{4} 25 - x^{2}