derivative of log_{3}(sin(x))

解答

\frac{d}{d x} (lo g_{3} (sin (x)))

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

求解步骤

\frac{d}{d x} (lo g_{3} (sin (x)))

使用对数计算法则:

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

= \frac{d}{d x} (\frac{ln ( sin ( x ) )}{ln ( 3 )})

将常数提出:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (sin (x)))

使用连锁律:

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

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

\frac{d}{d x} (sin (x)) = cos (x)

= \frac{1}{ln ( 3 )} \cdot \frac{1}{sin ( x )} cos (x)

化简

\frac{1}{ln ( 3 )} \cdot \frac{1}{sin ( x )} cos (x) : \frac{cot ( x )}{ln ( 3 )}

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

\int 5 x ln (1 + x) d x

a re a x^{2}, x

\frac{d}{d x} (8 sin (8 x))

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

x \to + 0 + lim (\frac{x ^{2}}{4} - \frac{2}{x})