(\partial)/(\partial x)(ycos(xlog_{e}(y)))

解答

\frac{\partial}{\partial x} (y cos (x lo g_{e} (y)))

- y sin (x ln (y)) ln (y)

求解步骤

\frac{\partial}{\partial x} (y cos (x lo g_{e} (y)))

化简

y cos (x lo g_{e} (y)) : y cos (x ln (y))

= \frac{\partial}{\partial x} (y cos (x ln (y)))

将

y

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} (cos (x ln (y)))

使用连锁律:

- sin (x ln (y)) \frac{\partial}{\partial x} (x ln (y))

= - sin (x ln (y)) \frac{\partial}{\partial x} (x ln (y))

\frac{\partial}{\partial x} (x ln (y)) = ln (y)

= y (- sin (x ln (y)) ln (y))

化简

= - y sin (x ln (y)) ln (y)

\frac{d y}{d t} = - 3 (y - 5)

x \to \infty lim (\frac{( \frac{x + 1}{x ^{3} + 2} )}{( \frac{x}{x ^{3}} )})

x \to 5 + lim (\frac{8}{x - 5})

\frac{d}{d x} (2 sin (2 x) - 2 cos (2 x) - \frac{1}{5} e^{x})

y = - 80 + 208