derivative (log_{6}(x))/(e^{4x)}

解答

导数

\frac{lo g _{6} ( x )}{e ^{4 x}}

\frac{1 - 4 x ln ( x )}{ln ( 6 ) e ^{4 x} x}

求解步骤

\frac{d}{d x} (\frac{lo g _{6} ( x )}{e ^{4 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} ( lo g _{6} ( x ) ) e ^{4 x} - \frac{d}{d x} ( e ^{4 x} ) lo g _{6} ( x )}{( e ^{4 x} ) ^{2}}

\frac{d}{d x} (lo g_{6} (x)) = \frac{1}{x ln ( 6 )}

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

= \frac{\frac{1}{x l n ( 6 )} e ^{4 x} - e ^{4 x} \cdot 4 lo g _{6} ( x )}{( e ^{4 x} ) ^{2}}

化简

\frac{\frac{1}{x l n ( 6 )} e ^{4 x} - e ^{4 x} \cdot 4 lo g _{6} ( x )}{( e ^{4 x} ) ^{2}} : \frac{1 - 4 x ln ( x )}{ln ( 6 ) e ^{4 x} x}

= \frac{1 - 4 x ln ( x )}{ln ( 6 ) e ^{4 x} x}

d er i v a t i v e f (t) = 8 t^{2} - t

3 x - 8 y x^{2} + 1 \frac{d y}{d x} = 0

\int_{7}^{e^{5}} \frac{1}{x} d x

\frac{\partial}{\partial x} (sin (x \cdot y))

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