derivative of sqrt(x)-1/(sqrt(x))

解答

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

\frac{1}{2 x} + \frac{1}{2 x ^{\frac{3}{2}}}

求解步骤

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

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

化简

= \frac{1}{2 x} + \frac{1}{2 x ^{\frac{3}{2}}}

\frac{d y}{d x} = e^{4 x - y}

\frac{d}{d x} (- x^{4})

h \to 0 lim (\frac{( - 4 + h ) + 4}{h})

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