derivative f(x)=sqrt(3x)ln(19x)

解答

导数

f (x) = 3 x ln (19 x)

\frac{3 ln ( 19 x )}{2 x} + \frac{3}{x}

求解步骤

\frac{d}{d x} (3 x ln (19 x))

使用微分乘法定则:

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

f = 3 x, g = ln (19 x)

= \frac{d}{d x} (3 x) ln (19 x) + \frac{d}{d x} (ln (19 x)) 3 x

\frac{d}{d x} (3 x) = \frac{3}{2 x}

\frac{d}{d x} (ln (19 x)) = \frac{1}{x}

= \frac{3}{2 x} ln (19 x) + \frac{1}{x} 3 x

化简

\frac{3}{2 x} ln (19 x) + \frac{1}{x} 3 x : \frac{3 ln ( 19 x )}{2 x} + \frac{3}{x}

= \frac{3 ln ( 19 x )}{2 x} + \frac{3}{x}

\int 3 x^{2} cos (2 x) d x

\frac{d y}{d x} - 2 x y = 4 x

\int 4 t^{3} - 8 t d t

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

\frac{d}{d x} (\frac{x - 9}{x + 9})