derivative of (8(4^x)/(x^4))

解答

\frac{d}{d x} (\frac{8 ( 4 ^{x} )}{x ^{4}})

\frac{16 ( ln ( 2 ) \cdot 4 ^{x} x - 2 ^{2 x + 1} )}{x ^{5}}

求解步骤

\frac{d}{d x} (\frac{8 ( 4 ^{x} )}{x ^{4}})

将常数提出:

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

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

使用微分除法定则:

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

= 8 \cdot \frac{\frac{d}{d x} ( 4 ^{x} ) x ^{4} - \frac{d}{d x} ( x ^{4} ) 4 ^{x}}{( x ^{4} ) ^{2}}

\frac{d}{d x} (4^{x}) = ln (2) \cdot 2^{2 x + 1}

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

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

化简

8 \cdot \frac{ln ( 2 ) \cdot 2 ^{2 x + 1} x ^{4} - 4 x ^{3} \cdot 4 ^{x}}{( x ^{4} ) ^{2}} : \frac{16 ( ln ( 2 ) \cdot 4 ^{x} x - 2 ^{2 x + 1} )}{x ^{5}}

= \frac{16 ( ln ( 2 ) \cdot 4 ^{x} x - 2 ^{2 x + 1} )}{x ^{5}}

\int_{0}^{\frac{1}{3}} \frac{5}{1 + 9 x ^{2}} d x

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

\frac{d}{d x} (x^{\frac{2}{3}} (x - 4))

\frac{d}{d x} ((2 x - 8)^{5})

l a pl a ce t r an s f or m f (t) = t^{2} e^{3 t}