derivative f(x)=-sqrt(x)

解答

导数

f (x) = - x

- \frac{1}{2 x}

求解步骤

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

将常数提出:

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

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

使用根式运算法则:

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

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

使用幂法则:

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

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

化简

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

= - \frac{1}{2 x}

t a y l or ln (\frac{x}{2}), 2

\int_{0}^{2} \frac{1}{( x ^{2} + 4 ) ^{2}} d x

\int (x^{2} - 3 x + 2) d x

\int \frac{1}{x - 3 x} d x

x \to 0 lim (x^{2} \cdot e^{\frac{1}{x}})