derivative of log_{4}(sec(x))

解答

\frac{d}{d x} (lo g_{4} (sec (x)))

\frac{tan ( x )}{2 ln ( 2 )}

求解步骤

\frac{d}{d x} (lo g_{4} (sec (x)))

使用对数计算法则:

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

= \frac{d}{d x} (\frac{ln ( sec ( x ) )}{ln ( 4 )})

将常数提出:

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

= \frac{1}{ln ( 4 )} \frac{d}{d x} (ln (sec (x)))

使用连锁律:

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

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

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= \frac{1}{ln ( 4 )} \cdot \frac{1}{sec ( x )} sec (x) tan (x)

化简

\frac{1}{ln ( 4 )} \cdot \frac{1}{sec ( x )} sec (x) tan (x) : \frac{tan ( x )}{2 ln ( 2 )}

= \frac{tan ( x )}{2 ln ( 2 )}

\frac{d}{d x} (3 x^{2} - \frac{1}{x ^{2}})

16 y^{^{''}} + 8 y^{^{'}} + y = 0

\int_{1}^{\infty} x e^{- 10 x} d x

x \to 0 lim (\frac{x + 1}{5 x})

a re a x^{2} - 2, 7