derivative of 8xln(x)

解答

\frac{d}{d x} (8 x ln (x))

8 (ln (x) + 1)

求解步骤

\frac{d}{d x} (8 x ln (x))

将常数提出:

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

= 8 \frac{d}{d x} (x ln (x))

使用微分乘法定则:

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

f = x, g = ln (x)

= 8 (\frac{d x}{d x} ln (x) + \frac{d}{d x} (ln (x)) x)

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

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

= 8 (1 \cdot ln (x) + \frac{1}{x} x)

化简

8 (1 \cdot ln (x) + \frac{1}{x} x) : 8 (ln (x) + 1)

= 8 (ln (x) + 1)

\int \frac{x}{1 + 3 x ^{2}} d x

\frac{d}{d x} (3 - 3 x^{2} + 5 x + 1)

\int (3 e^{x} + 8 x^{3} + 4 x) d x

\frac{d}{d x} (\frac{3}{4 x})

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