derivative of log_{5}(6x^3)

解答

\frac{d}{d x} (lo g_{5} (6 x^{3}))

\frac{3}{ln ( 5 ) x}

求解步骤

\frac{d}{d x} (lo g_{5} (6 x^{3}))

使用对数计算法则:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( 6 x ^{3} )}{ln ( 5 )})

将常数提出:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (6 x^{3}))

使用连锁律:

\frac{1}{6 x ^{3}} \frac{d}{d x} (6 x^{3})

= \frac{1}{6 x ^{3}} \frac{d}{d x} (6 x^{3})

\frac{d}{d x} (6 x^{3}) = 18 x^{2}

= \frac{1}{ln ( 5 )} \cdot \frac{1}{6 x ^{3}} \cdot 18 x^{2}

化简

\frac{1}{ln ( 5 )} \cdot \frac{1}{6 x ^{3}} \cdot 18 x^{2} : \frac{3}{ln ( 5 ) x}

= \frac{3}{ln ( 5 ) x}

s l o p e y = \frac{1}{x - 4}, at x = 9

\int 7 e^{2} d x

\int_{0}^{1} \frac{1}{( x ^{2} + 1 )} d x

\int 5 a x^{3} x d x

\int ln (y^{2}) d y