derivative of (x^{3.8}/(6^x))

解答

\frac{d}{d x} (\frac{x ^{3.8}}{6 ^{x}})

\frac{x ^{2.8} ( 3.8 - 1.79175 \dots x )}{6 ^{x}}

求解步骤

\frac{d}{d x} (\frac{x ^{3.8}}{6 ^{x}})

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} ( x ^{3.8} ) 6 ^{x} - \frac{d}{d x} ( 6 ^{x} ) x ^{3.8}}{( 6 ^{x} ) ^{2}}

\frac{d}{d x} (x^{3.8}) = 3.8 x^{2.8}

\frac{d}{d x} (6^{x}) = 6^{x} ln (6)

= \frac{3.8 x ^{2.8} \cdot 6 ^{x} - 6 ^{x} ln ( 6 ) x ^{3.8}}{( 6 ^{x} ) ^{2}}

化简

\frac{3.8 x ^{2.8} \cdot 6 ^{x} - 6 ^{x} ln ( 6 ) x ^{3.8}}{( 6 ^{x} ) ^{2}} : \frac{x ^{2.8} ( 3.8 - 1.79175 \dots x )}{6 ^{x}}

= \frac{x ^{2.8} ( 3.8 - 1.79175 \dots x )}{6 ^{x}}

d er i v a t i v e tan^{2} (6 θ)

in v erse l a pl a ce \frac{1}{s ^{3} ( s - 1 )}

\frac{\partial}{\partial x} (cos (2 y - 2 x))

\int (3 x^{2} - 2 x + 1) (x^{3} - x^{2} + x)^{4} d x

x \to 3 lim (x^{2} + 7 x - 5)