(\partial)/(\partial x)(sqrt(x)ln(t))

解答

\frac{\partial}{\partial x} (x ln (t))

\frac{ln ( t )}{2 x}

求解步骤

\frac{\partial}{\partial x} (x ln (t))

将

t

视为常数

将常数提出:

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

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

使用根式运算法则:

a = a^{\frac{1}{2}}

= ln (t) \frac{\partial}{\partial x} (x^{\frac{1}{2}})

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= ln (t) \frac{1}{2} x^{\frac{1}{2} - 1}

化简

ln (t) \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{ln ( t )}{2 x}

= \frac{ln ( t )}{2 x}

5 y^{^{'}} - 15 x^{2} = 0

n \to 10 lim ([1 + (\frac{1}{n})]^{n})

\frac{d}{d x} (2 (1 - x)^{- 3})

x \to 0 lim (\frac{5 ^{x} - 4 ^{x}}{x})

d er i v a t i v e \frac{2 x + 3}{3 x + 2}