derivative of (9x/(sqrt(x)))

解答

\frac{d}{d x} (\frac{9 x}{x})

\frac{9}{2 x}

求解步骤

\frac{d}{d x} (\frac{9 x}{x})

化简

\frac{9 x}{x} : 9 x

= \frac{d}{d x} (9 x)

将常数提出:

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

= 9 \frac{d}{d x} (x)

使用根式运算法则:

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

= 9 \frac{d}{d x} (x^{\frac{1}{2}})

使用幂法则:

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

= 9 \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

化简

9 \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{9}{2 x}

= \frac{9}{2 x}

x \to 0 + lim (x^{x^{8}})

\int 36 x^{3} (3 x^{4} + 3)^{5} d x

y \to 0 lim (\frac{0}{y})

t an g e n t f (x) = (x^{2} - 3) (x^{3} - 2 x), at x = - 2

\frac{\partial}{\partial x} (x e^{y} + x^{2} cos (y))