derivative of log_{7}(ln(x))

解答

\frac{d}{d x} (lo g_{7} (ln (x)))

\frac{1}{ln ( 7 ) x ln ( x )}

求解步骤

\frac{d}{d x} (lo g_{7} (ln (x)))

使用对数计算法则:

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

= \frac{d}{d x} (\frac{ln ( ln ( x ) )}{ln ( 7 )})

将常数提出:

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

= \frac{1}{ln ( 7 )} \frac{d}{d x} (ln (ln (x)))

使用连锁律:

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

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

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

= \frac{1}{ln ( 7 )} \cdot \frac{1}{ln ( x )} \cdot \frac{1}{x}

化简

\frac{1}{ln ( 7 )} \cdot \frac{1}{ln ( x )} \cdot \frac{1}{x} : \frac{1}{ln ( 7 ) x ln ( x )}

= \frac{1}{ln ( 7 ) x ln ( x )}

\int e^{a r c c o s (x)} d x

\int 2 x - \frac{1}{x ^{2}} d x

\int 2^{x} + x^{2} d x

\frac{\partial}{\partial z} (yz - ln (x + z))

x \to - \infty lim (7)