derivative log_{5}(sqrt(x^2-4))

解答

导数

lo g_{5} (x^{2} - 4)

\frac{x}{ln ( 5 ) ( x ^{2} - 4 )}

求解步骤

\frac{d}{d x} (lo g_{5} (x^{2} - 4))

使用对数计算法则:

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

= \frac{d}{d x} (\frac{ln ( x ^{2} - 4 )}{ln ( 5 )})

将常数提出:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (x^{2} - 4))

使用连锁律:

\frac{1}{x ^{2} - 4} \frac{d}{d x} (x^{2} - 4)

= \frac{1}{x ^{2} - 4} \frac{d}{d x} (x^{2} - 4)

\frac{d}{d x} (x^{2} - 4) = \frac{x}{x ^{2} - 4}

= \frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{2} - 4} \cdot \frac{x}{x ^{2} - 4}

化简

\frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{2} - 4} \cdot \frac{x}{x ^{2} - 4} : \frac{x}{ln ( 5 ) ( x ^{2} - 4 )}

= \frac{x}{ln ( 5 ) ( x ^{2} - 4 )}

\frac{d}{d θ} (5 sin (2 θ))

y^{^{''}} + 3 y = 0

\int \frac{x ^{2} + 2 x + 3}{x ^{3} - x} d x

\int_{2}^{3} \frac{1}{x - 1} d x

x \to - 4 lim (6 x + 11)