derivative of (x^4/8 ln(x)-(x^4)/(32))

解答

\frac{d}{d x} (\frac{x ^{4}}{8} ln (x) - \frac{x ^{4}}{32})

\frac{x ^{3} ln ( x )}{2}

求解步骤

\frac{d}{d x} (\frac{x ^{4}}{8} ln (x) - \frac{x ^{4}}{32})

化简

\frac{x ^{4}}{8} ln (x) - \frac{x ^{4}}{32} : \frac{x ^{4} ln ( x )}{8} - \frac{x ^{4}}{32}

= \frac{d}{d x} (\frac{x ^{4} ln ( x )}{8} - \frac{x ^{4}}{32})

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{x ^{4} ln ( x )}{8}) - \frac{d}{d x} (\frac{x ^{4}}{32})

\frac{d}{d x} (\frac{x ^{4} ln ( x )}{8}) = \frac{1}{8} (4 x^{3} ln (x) + x^{3})

\frac{d}{d x} (\frac{x ^{4}}{32}) = \frac{x ^{3}}{8}

= \frac{1}{8} (4 x^{3} ln (x) + x^{3}) - \frac{x ^{3}}{8}

化简

\frac{1}{8} (4 x^{3} ln (x) + x^{3}) - \frac{x ^{3}}{8} : \frac{x ^{3} ln ( x )}{2}

= \frac{x ^{3} ln ( x )}{2}

t an g e n t y = \frac{8}{x + 1}

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

\frac{d}{d x} (\frac{cos ( 2 x )}{x})

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

\frac{d}{d x} (\frac{( 6 e ^{x} )}{2 e ^{x} + 1})