derivative f(x)=sqrt(log_{a)(x)}

解答

导数

f (x) = lo g_{a} (x)

\frac{1}{2 x ln ( a ) lo g _{a} ( x )}

求解步骤

\frac{d}{d x} (lo g_{a} (x))

使用连锁律:

\frac{1}{2 lo g _{a} ( x )} \frac{d}{d x} (lo g_{a} (x))

= \frac{1}{2 lo g _{a} ( x )} \frac{d}{d x} (lo g_{a} (x))

\frac{d}{d x} (lo g_{a} (x)) = \frac{1}{x ln ( a )}

= \frac{1}{2 lo g _{a} ( x )} \cdot \frac{1}{x ln ( a )}

化简

\frac{1}{2 lo g _{a} ( x )} \cdot \frac{1}{x ln ( a )} : \frac{1}{2 x ln ( a ) lo g _{a} ( x )}

= \frac{1}{2 x ln ( a ) lo g _{a} ( x )}

\frac{\partial}{\partial x} (x^{\frac{1}{2}} + y)

t an g e n t y = 4 e^{x}

\frac{\partial}{\partial t} (t^{2})

x \to 0 lim (arctan (6 x))

x \to - 3 lim (5 - x)