derivative (0.3(5^x))/(x^3)

解答

导数

\frac{0.3 ( 5 ^{x} )}{x ^{3}}

\frac{0.3 \cdot 5 ^{x} ( 1.60943 \dots x - 3 )}{x ^{4}}

求解步骤

\frac{d}{d x} (\frac{0.3 \cdot 5 ^{x}}{x ^{3}})

将常数提出:

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

= 0.3 \frac{d}{d x} (\frac{5 ^{x}}{x ^{3}})

使用微分除法定则:

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

= 0.3 \cdot \frac{\frac{d}{d x} ( 5 ^{x} ) x ^{3} - \frac{d}{d x} ( x ^{3} ) 5 ^{x}}{( x ^{3} ) ^{2}}

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

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

= 0.3 \cdot \frac{5 ^{x} ln ( 5 ) x ^{3} - 3 x ^{2} \cdot 5 ^{x}}{( x ^{3} ) ^{2}}

化简

0.3 \cdot \frac{5 ^{x} ln ( 5 ) x ^{3} - 3 x ^{2} \cdot 5 ^{x}}{( x ^{3} ) ^{2}} : \frac{0.3 \cdot 5 ^{x} ( 1.60943 \dots x - 3 )}{x ^{4}}

= \frac{0.3 \cdot 5 ^{x} ( 1.60943 \dots x - 3 )}{x ^{4}}

t a y l or cos (x^{2}), 0

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