(\partial)/(\partial x)(xln(y+x))

解答

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

ln (y + x) + \frac{x}{y + x}

求解步骤

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

将

y

视为常数

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (y + x)

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (ln (y + x)) = \frac{1}{y + x}

= 1 \cdot ln (y + x) + \frac{1}{y + x} x

化简

1 \cdot ln (y + x) + \frac{1}{y + x} x : ln (y + x) + \frac{x}{y + x}

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

y^{^{'}} = e (- 2 t) - y

(cos (3 x))^{^{'}}

\frac{d}{d x} (e^{x} - 1 - x)

\frac{d y}{d x} = e^{- x^{2}}

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