derivative of (ln(x)/(x^{5/4)})

解答

\frac{d}{d x} (\frac{ln ( x )}{x ^{\frac{5}{4}}})

\frac{4 - 5 ln ( x )}{4 x ^{\frac{9}{4}}}

求解步骤

\frac{d}{d x} (\frac{ln ( x )}{x ^{\frac{5}{4}}})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ln ( x ) ) x ^{\frac{5}{4}} - \frac{d}{d x} ( x ^{\frac{5}{4}} ) ln ( x )}{( x ^{\frac{5}{4}} ) ^{2}}

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

\frac{d}{d x} (x^{\frac{5}{4}}) = \frac{5 x ^{\frac{1}{4}}}{4}

= \frac{\frac{1}{x} x ^{\frac{5}{4}} - \frac{5 x ^{\frac{1}{4}}}{4} ln ( x )}{( x ^{\frac{5}{4}} ) ^{2}}

化简

\frac{\frac{1}{x} x ^{\frac{5}{4}} - \frac{5 x ^{\frac{1}{4}}}{4} ln ( x )}{( x ^{\frac{5}{4}} ) ^{2}} : \frac{4 - 5 ln ( x )}{4 x ^{\frac{9}{4}}}

= \frac{4 - 5 ln ( x )}{4 x ^{\frac{9}{4}}}

\int y cos (y) sin^{2} (y) d y

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d er i v a t i v e [x + (x + sin^{2} (x))^{5}]^{7}

d er i v a t i v e 6 (2 x^{3} + 3) 6 x^{2}