derivative sqrt(35x)ln(10x)

解答

导数

35 x ln (10 x)

\frac{35 ln ( 10 x )}{2 x} + \frac{35}{x}

求解步骤

\frac{d}{d x} (35 x ln (10 x))

使用微分乘法定则:

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

f = 35 x, g = ln (10 x)

= \frac{d}{d x} (35 x) ln (10 x) + \frac{d}{d x} (ln (10 x)) 35 x

\frac{d}{d x} (35 x) = \frac{35}{2 x}

\frac{d}{d x} (ln (10 x)) = \frac{1}{x}

= \frac{35}{2 x} ln (10 x) + \frac{1}{x} 35 x

化简

\frac{35}{2 x} ln (10 x) + \frac{1}{x} 35 x : \frac{35 ln ( 10 x )}{2 x} + \frac{35}{x}

= \frac{35 ln ( 10 x )}{2 x} + \frac{35}{x}

(1 + x^{4}) d y + x (1 + 4 y^{2}) d x = 0, y (1) = 0

4 y^{^{''}} - y = 1

\int e^{3 x} d x

t an g e n t (x^{2} - 9)^{2}

y^{^{''}} - 3 y^{^{'}} - 10 y = 4, y (0) = 0, y^{^{'}} (0) = 0