derivative xlog_{3}(x)

解答

导数

x lo g_{3} (x)

lo g_{3} (x) + \frac{1}{ln ( 3 )}

求解步骤

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

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = lo g_{3} (x)

= \frac{d x}{d x} lo g_{3} (x) + \frac{d}{d x} (lo g_{3} (x)) x

\frac{d x}{d x} = 1

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

= 1 \cdot lo g_{3} (x) + \frac{1}{x ln ( 3 )} x

化简

1 \cdot lo g_{3} (x) + \frac{1}{x ln ( 3 )} x : lo g_{3} (x) + \frac{1}{ln ( 3 )}

= lo g_{3} (x) + \frac{1}{ln ( 3 )}

\frac{\partial}{\partial x} (4 y cos (x y))

d er i v a t i v e x tan (x)

\int_{\frac{π}{2}}^{π} sin^{2} (x) d x

t an g e n t 5 - 4 x^{3}

l a pl a ce t r an s f or m {y}